Stochastic Poisson Process Research Articles

Some Results of Stochastic Differential Equations

In this paper, there are two aims: one is Schauder and Sobolev estimates for the one-dimensional heat equation; the other is the stabilization of differential equations by stochastic feedback control based on discrete-time state observations. The nonhomogeneous Poisson stochastic process is used to show how knowing Schauder and Sobolev estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs. The properties of a jump process is used. The stabilization of differential equations by stochastic feedback control is based on discrete-time state observations. Firstly, the stability results of the auxiliary system is established. Secondly, by comparing it with the auxiliary system and using the continuity method, the stabilization of the original system is obtained. Both parts focus on the impact of probability theory.

Simple Moment Generating Function Optimisation Technique to Design Optimum Electronic Filter for Underwater Wireless Optical Communication Receiver

This paper introduces a new simple moment-generating function (MGF) design modelling method to conclude an optimum filter to maximize the Q-factor and increase the link communication span. This approach mitigates the pulse temporal dispersion, particularly the underwater wireless optical communication (UWOC) systems. Hence, some form of equalizing filter design is highly desirable. The model solution environment includes a Double Gamma Function (DGF) water channel impulse response, intersymbol interference (ISI), stochastic Poisson process, and additive Gaussian thermal noise (AGTN). The optimal filters exhibit temporal profiles comparable to those derived by published works based on complex Chernoff Bound (CB) and Modified Chernoff Bound (MCB) methods. The results show the impact of the optimum filter at a signal level and optical receiver level utilizing Eye-Diagrams and BER vs. Q-Factor, respectively. The computation involves four different UWOC propagation channel models for Coastal and Harbor waters. One of the main conclusions indicates that the optimum filter manages the temporal dispersion due to the ISI impairment correctly. Also, the proposed optimum filter reduces eye-opening and the corresponding Q-Factor by less than 15% for a five-times increase in pulse width for the same transmitted optical power level.

Evaluation Method of Fatigue Life for Asphalt Pavement on the Steel Bridge Deck Based on the Inhomogeneous Poisson Stochastic Process.

The paving layer on the steel box girder bridge deck is widely used when constructing pavements for steel bridges. Owing to the orthotropic feature of steel decks, a transverse clapboard and rib can lead to a concentration of stress. Consequently, fatigue cracks are often identified in asphalt concrete pavement layers due to re-compaction caused by heavy vehicles. This study aims to derive an evaluation method of fatigue life for asphalt pavement based on the inhomogeneous Poisson stochastic process in view of the highly random and uncertain working conditions of layered composite structures. According to the inhomogeneous Poisson stochastic process, along with Miner's fatigue damage accumulation theory and the linear elastic fracture mechanics theory, the fatigue life formula could be deduced. Meanwhile, fatigue experiments for asphalt concrete are designed to investigate the correlation between the theoretical formula and the actual fatigue damage life of the material. Compared with the test, the accuracy error is within 10%, which is better than other traditional methods. Therefore, the fatigue life prediction model could better reflect the loading order effect and the interaction between loads, providing a new path for the fatigue reliability design of steel bridge deck asphalt pavement.

Valuation of Commodity-Linked Bond with Stochastic Convenience Yield, Stochastic Volatility, and Credit Risk in an Intensity-Based Model

In this study, we consider an intensity-based model for pricing a commodity-linked bond with credit risk. Recently, the pricing of a commodity-linked bond with credit risk under the structural model has been studied. We extend the result using an intensity-based model, stochastic volatility model, and stochastic convenience yield model. In the intensity-based model, the credit event by the counterparty occurs at the time of first jump in a stochastic Poisson process, in which intensity is modeled as the sum of two CIR prosesses. We assume that the underlying asset follows the stochastic volatility and convenience yield models. Using the measure change technique, we explicitly derive the commodity-linked bond pricing formula in the proposed model. As a result, we provide the explicit solution for the price of the commodity-linked bond with stochastic convenience yield, stochastic volatility, and credit risk as single integrations. In addition, we present several examples to demonstrate the effects of significant parameters on the value of commodity-linked bond using numerical integration. In particular, examples are provided, focusing on the behavior of prices based on effects of recovery rate.

Assessment of the impact of climate change and flooding on bridges and surrounding area

Climate change has the potential to significantly impact transportation infrastructure performance. Bridges crossing rivers are designed to withstand a maximum flood level (design flood) considering the expected frequencies and magnitudes of floods in the area. The design flood level ensures the safety of the bridge without being damaged against historical flooding levels. However, flood magnitude and/or frequency are expected to increase in some regions due to climate change, and therefore, bridges may not be able to maintain their serviceability and safety, resulting in significant risk to users and economic losses. This problem is approached in this paper by investigating the effects of flooding and climate change on bridges crossing rivers and surrounding areas. The input of the proposed methodology is the river flow for various climate change scenarios as well as the topography and bridge characteristics. Flood frequency analysis is used to provide information about the magnitude and frequency of annual maximum river discharges under a changing climate. Afterwards, several risk assessment indicators are computed for the bridge and its surrounding area. In addition, stochastic Poisson process is integrated to account for the randomness of floods arrivals and to investigate stochastically the probability of exceeding the design flood level. The proposed methodology is illustrated with a case study in the United Kingdom. The results indicate that the risk of flooding, and associated consequences, would increase for the case study when considering more pessimistic climate change scenarios. Findings from this study can be used to inform decision making for improving bridges’ resilience.

Data Mining Approach Based on Hierarchical Gaussian Mixture Representation Model

Infinite Gaussian mixture process is a model that computes the Gaussian mixture parameters with order. This process is a probability density distribution with adequate training data that can converge to the input density curve. In this paper, we propose a data mining model namely Beta hierarchical distribution that can solve axial data modeling. A novel hierarchical Two-Hyper-Parameter Poisson stochastic process is developed to solve grouped data modelling. The solution uses data mining techniques to link datum in groups by linking their components. The learning techniques are novel presentations of Gaussian modelling that use prior knowledge of the representation hyper-parameters and approximate them in a closed form. Experiments are performed on axial data modeling of Arabic Script classification and depict the effectiveness of the proposed method using a hand written benchmark dataset which contains complex handwritten Arabic patterns. Experiments are also performed on the application of facial expression recognition and prove the accuracy of the proposed method using a benchmark dataset which contains eight different facial expressions.

Relaying Data With Joint Optimization of Energy and Delay in Cluster-Based UAV-Assisted VANETs

Vehicular networks are known for their dynamic topology, high mobility, and frequent disconnections. Unmanned aerial vehicles (UAVs) have been recently used as instant communication relays to bridge the communication gaps between terrestrial vehicles to improve connectivity in vehicular networks and overcome the aforementioned problems. Despite the existing work in the literature where each vehicle connects directly to UAVs, this work studies how clustering and different densities of vehicles affect delay and energy efficiency in a UAV-based vehicular network integrated with 5G technology. Consequently, this work addresses the problem of UAV enabling vehicular ad-hoc networks (VANETs) in a highway scenario, where UAVs serve as an effective complement to forward data packets between vehicles in the absence of sufficient fixed infrastructures in an emergency situation. The main objective of this work is to minimize the delay while maximizing the energy efficiency by minimizing the power consumption and maximizing the total data rate under realistic conditions, while nonorthogonal multiple access (NOMA) is also adopted as an alternative answer for the effective utilization of limited bandwidth. The free-flowing traffic follows a Poisson stochastic process where each vehicle is assigned a random speed selected from a truncated Gaussian distribution. To this end, a novel modification of fast global <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -means is adopted to partition vehicles, allowing communication between clusters by vehicle-to-vehicle links, while data packets between clusters are relayed through UAVs. By computing the convex approximation of the objective function and the constraints, the original problem with the mixed-integer, nonconvex, and nonlinear form is solved by the proposed iterative inner penalty function algorithm. Finally, extensive simulations are conducted to validate the superiority of the proposed method in terms of various metrics. The results indicate that the relaying task in the proposed UAV-assisted VANET based on 5G technology is perfectly suited to enhance the network connectivity.

Risk-Acceptance Criteria in Occupational Health and Safety Risk-Assessment—The State-of-the-Art through a Systematic Literature Review

The utilization of risk acceptance criteria (RAC) can help a business to judge whether the risk level concerning any process involved in its working environment is acceptable or not, especially when the risk has a significant societal impact. Thus, the main intention of this study is to make known the current state-of-the-art concerning RACs and to propose new interpretations of it by surveying, for first time, the scientific literature about the RACs associated with the occupational health and safety (OHS) risk-assessment methodologies (RAA). A second objective of this work is the attainment of a prediction for the evolution of the quantity of the publications concerning OHS-RACs, and a third one is the derivation of an algorithm (via a flow-chart) in order to illustrate the process of the formation of new OHS-RACs. The work consists of two parts, (a) exploring and presenting methods of developing RACs in OHS; (b) classifying, analyzing, and benchmarking relevant published scientific articles by surveying the Scopus data base with proper search-hints, through a time interval of 20 years (January2000–December 2019). The review has defined a plethora of RAC-papers with reference to OHS, which is a remarkable percentage in comparison with the other fields aggregated, and this outcome proves that the issue of utilizing RACs is fundamental for the field of OHS. Additionally, it has been deduced that, day after day, there is an increasing tendency for the scientific community to develop and use RACs in the field of occupational safety, as this is evident by their frequent reference to the risk analysis and assessment (RAA) process. Our specific research methodology has been compatible with the PRISMA protocol. A prediction for the evolution of the quantity of the OHS-RAC publications is also given by confirming the Poisson stochastic process. Finally, we propose a generic guideline framework that can contribute to the establishment of new empirically-generated OHS-RACs.

Differences in the number of de novo mutations between individuals are due to small family-specific effects and stochasticity.

The number of de novo mutations (DNMs) in the human germline is correlated with parental age at conception, but this explains only part of the observed variation. We investigated whether there is a family-specific contribution to the number of DNMs in offspring. The analysis of DNMs in 111 dizygotic twin pairs did not identify a substantial family-specific contribution. This result was corroborated by comparing DNMs of 1669 siblings to those of age-matched unrelated offspring following correction for parental age. In addition, by modeling DNM data from 1714 multi-offspring families, we estimated that the family-specific contribution explains ∼5.2% of the variation in DNM number. Furthermore, we found no substantial difference between the observed number of DNMs and those predicted by a stochastic Poisson process. We conclude that there is a small family-specific contribution to DNM number and that stochasticity explains a large proportion of variation in DNM counts.

Stochastic Integrals and Random Sums of Power Contractions in Systemics

Stochastic integrals, random sums, random contractions, and selfdecomposable random variables constitute fundamental concepts of probability theory with significant applications in several areas of systemics. The main results of the paper are a characterization of a selfdecomposable distribution and a formulation of a Poisson random sum of power contractions. These results are established by incorporating a type of stochastic integral for a continuous in probability, homogeneous stochastic process with independent increments, and the same type of stochastic integral for a compound Poisson stochastic process with positive jumps. Interpretations of the results in treatment of risks threatening various systems are also provided.

Atomistic-to-meso multi-scale data-driven graph surrogate modeling of dislocation glide

From their birth in the manufacturing process, materials inherently contain defects that affect the mechanical behavior across multiple length and time-scales, including vacancies, dislocations, voids and cracks. Understanding, modeling, and real-time simulation of the underlying stochastic micro-structure defect evolution is therefore vital towards multi-scale coupling and propagating numerous sources of uncertainty from atomistic to eventually aging continuum mechanics. We develop a graph-based surrogate model of dislocation glide for computation of stochastic dislocation mobility. We model an edge dislocation as a random walker, jumping between neighboring nodes of a graph following a Poisson stochastic process. The network representation functions as a coarse-graining of a molecular dynamics simulation that provides dislocation trajectories for an empirical computation of jump rates. With this construction, we recover the original atomistic mobility estimates, with remarkable computational speed-up and accuracy. Furthermore, the underlying stochastic process provides the statistics of dislocation mobility associated to the original molecular dynamics simulation, allowing an efficient propagation of material parameters and uncertainties across the scales.

A Stationary Drake Equation Distribution as a Balance of Birth-death Processes

Abstract Previous critiques of the Drake Equation have highlighted its deterministic nature, implying that the number of civilizations is the same at all times. Here, I build upon earlier work and present a stochastic formulation. The birth of civilizations within the galaxy is modeled as following a uniform rate (Poisson) stochastic process, with a mean rate of λ C . Each then experiences a constant hazard rate of collapse, which defines an exponential distribution with rate parameter λ L . Thus, the galaxy is viewed as a frothing landscape of civilization birth and collapse. Under these assumptions, I show that N in the Drake Equation must follow another Poisson distribution, with a mean rate (λ C /λ L ). This is used to demonstrate why the Copernican Principle does not allow one to infer N, as well evaluating the algebraic probability of being alone in the galaxy.

On Some Local Asymptotic Properties of Sequences with a Random Index

Random sequences with random or stochastic indices controlled by a doubly stochastic Poisson process are considered in this paper. A Poisson stochastic index process (PSI-process) is a random process with the continuous time ψ(t) obtained by subordinating a sequence of random variables (ξj), j = 0, 1, …, by a doubly stochastic Poisson process Π1(tλ) via the substitution ψ(t) = $${{\xi }_{{{{\Pi }_{1}}(t\lambda )}}}$$ , t $$ \geqslant $$ 0, where the random intensity λ is assumed independent of the standard Poisson process Π1. In this paper, we restrict our consideration to the case of independent identically distributed random variables (ξj) with a finite variance. We find a representation of the fractional Ornstein–Uhlenbeck process with the Hurst exponent H ∈ (0, 1/2) introduced and investigated by R. Wolpert and M. Taqqu (2005) in the form of a limit of normalized sums of independent identically distributed PSI-processes with an explicitly given distribution of the random intensity λ. This fractional Ornstein–Uhlenbeck process provides a local, at t = 0, mean-square approximation of the fractional Brownian motion with the same Hurst exponent H ∈ (0, 1/2). We examine in detail two examples of PSI-processes with the random intensity λ generating the fractional Ornstein–Uhlenbeck process in the Wolpert and Taqqu sense. These are a telegraph process arising when ξ0 has a Rademacher distribution ±1 with the probability 1/2 and a PSI-process with the uniform distribution for ξ0. For these two examples, we calculate the exact and the asymptotic values of the local modulus of continuity for a single PSI-process over a small fixed time span.

Vehicle Cooperative Network Model Based on Hypergraph in Vehicular Fog Computing.

In this paper, we propose an optimization framework of vehicular fog computing and a cooperation vehicular network model. We aim to improve the performance of vehicular fog computing and solve the problem that the data of the vehicle collaborative network is difficult to obtain. This paper applies the hypergraph theory to study the underlying structure, considering the social characteristics of the vehicles and vehicle communication. Since the vehicles join the network in accordance with the Poisson process law, the model is analyzed by using Poisson stochastic process and mean field theory. This paper uses MATLAB to simulate the evolution process of cooperative networks. The results show that the vehicle’s super-degree in vehicular fog computing has scale-free characteristics. Through this model, the vehicle cooperation situation can be analyzed, and the vehicle dynamics can be accurately predicted to further improve the performance of vehicular fog computing. The model can be transformed into some complex network models by adjusting the parameters. It has strong universality and has certain reference significance for the research on the related characteristics of VANETs and the theoretical research of the cooperative network.

On some local asymptotic properties of sequences with a random index

«Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия» — научно-теоретический рецензируемый журнал, публикующий исследования в области математики, механики и астрономии, а также математического моделирования.

Time-dependent reliability analysis of the motor hanger for EMU based on stochastic process

Purpose Most of the previous work on reliability analysis was based on the traditional reliability theory. The calculated results can only reflect the reliability of components at a specific time, which neglects the uncertainty of load and resistance over time. The purpose of this paper is to develop a time-dependent reliability analysis approach based on stochastic process to deal with the problem and apply it to the structural design of railway vehicle components. Design/methodology/approach First, the parametric model of motor hanger for electric multiple unit (EMU) is established by ANSYS parametric design language, and its structural stress is analyzed according to relevant standards. The Latin hypercube method is used to analyze the sensitivity of the structure, and the uncertainty parameters (sizes and loads) which have great influence on the structural strength are determined. The D-optimal experimental design is carried out to establish the polynomial response surface function, which characterizes the relationship between uncertainty parameters and structural stress. Second, the Poisson stochastic process is adopted to describe the number of loads acting, and the Monte Carlo method is used to obtain the load acting history according to its probability distribution characteristics. The load history is introduced into the response surface function and the uncertainty of other parameters is considered at the same time, and the stress history of the motor hanger is obtained. Finally, the degradation process of structural resistance is described by a Gamma stochastic process, and the time-dependent reliability of the motor hanger is calculated based on the reliability theory. Findings Time and the uncertainties of parameters have great impact on reliability. The results of reliability decrease with time fluctuation are more reasonable, stable and credible than traditional methods. Practical implications In this paper, the proposed method is applied to the structural design of the motor hanger for EMU, which has a good guiding significance for accurately evaluating whether if the design meets the reliability requirements. Originality/value The value of this paper is that the method takes both the randomness of load over time and the uncertainty of structural parameters in the design and manufactures process into consideration, and describes the monotonous degradation characteristics of structural resistance. At the same time, the time-dependent reliability of mechanical components is calculated by a response surface method. It not only improves the accuracy of reliability analysis, but also improves the analysis efficiency and solves the problem that the traditional reliability analysis method can only reflect the static reliability of components.

On the Probabilistic Characteristics of A Two Lane Slab-Type-Bridge Response Due to Traffic Flow

In this study, the two first probabilistic characteristics of a two lane slab-type-bridge response due to traffic flow is investigated. A two lane slab-type-bridge is modelled by a Simply Supported (SS) thin rectangular plate with two separate rectilinear paths. The modelling of the traffic flow is based on the assumption that two opposite series of vehicles of random weights arrive at the bridge at random times that constitute the Poisson stochastic process and with the stochastic velocities. The expected value and the standard deviation of the bridge deflection are obtained. We demonstrate that the bridge safety strongly depends to the mean value and to the standard deviation of the vehicles velocities.

Gaussian process regression modeling of wind turbines lightning incidence with LLS information

This paper presents a machine learning (ML) approach to wind turbine (WT) lightning incidence analysis in complex terrain, based on the information obtained from a lightning location system (LLS). A particular ML model of the WTs lightning incidence is developed, using Bayesian statistical learning and Gaussian process regression, and trained on the actual LLS data. The model is developed around a known proposition that the lightning strike frequency data are emanating from a Poisson stochastic process. It further makes use of an attractive radius concept of lightning attachment, employs a sophisticated analysis of the WT effective height—which leverages terrain elevation data—and introduces spatial autocorrelation of lightning strikes. It provides a probabilistic risk assessment of WT lightning damage, along with a statistical measures of the associated monetized financial losses. Proposed ML model benefits from the Bayesian ability to quantify uncertainty of model parameters, and employ hierarchical model structure that informs model parameters through the mutual higher-level hyperpriors. Proposed model enables both investors and insurance companies to asses risks associated with lightning incidence to WTs, considering historical LLS data and future wind farm installation locations.

Exact conditional maximized sequential probability ratio test adjusted for covariates

Sequential analysis is now commonly used for post-market drug and vaccine safety surveillance, and a Poisson stochastic process is typically used for rare adverse events. The conditional maximized sequential probability ratio test, CMaxSPRT, is a powerful tool when there is uncertainty in the estimated expected counts under the null hypothesis. This paper derives exact critical values for CMaxSPRT, as well as statistical power and expected time to signal. This is done for both continuous and group sequential analysis, and for different rejection boundaries. It is also shown how to adjust for covariates in the sequential design. A table of critical values is provided for selected parameters and rejection boundaries, while new functions in the R Sequential package can be used for other calculations. In addition, the method is illustrated for monitoring adverse events after pediarix vaccination data.

Optimizing dynamic survivability and security of replicated data in cloud systems under co-residence attacks

Utilizing the virtualization technology, multiple virtual machines (VMs) can be created on a single physical server for different tasks, enabling cost-effective resource sharing in cloud computing systems. However, this co-resident VM architecture can be exploited by malicious attackers, posing unique survivability and security risks for cloud users. This paper addresses one of such risks called co-residence attacks, where a malicious attacker can steal or corrupt a user's sensitive information through co-residing the attacker's VM with the target user's VM on the same physical server. We model users’ data protection policy in which sensitive data are replicated and stored on different VMs to enhance data survivability. Both user's and attacker's VMs are distributed among cloud servers at random. The arrival of attacker's requests for creating VMs is modeled by a Poisson stochastic process. We propose a probabilistic model to obtain dynamic data survivability and security indices. Based on the suggested evaluation model, dynamic data replication policies are analyzed and optimized. Numerical examples are presented to demonstrate impacts of different model parameters on the dynamic data survivability and security.