Applications Of Stochastic Processes Research Articles

Application of Stochastic Processes in Financial Market Models

This paper explores the significant role of stochastic processes in financial modeling, tracing the evolution from basic Brownian motion to sophisticated stochastic differential equations used in modern financial markets. Beginning with the historical development of Brownian motion, identified by Robert Brown and later mathematically modeled by Louis Bachelier for stock price fluctuations, the paper outlines its foundational influence on the Efficient Market Hypothesis and the random walk theory. The extension of these concepts in the Black-Scholes model for option pricing highlights the practical applications of these theories in predicting financial outcomes. The discussion progresses to geometric Brownian motion (GBM) and its crucial role in stock price modeling, emphasizing its use in Monte Carlo simulations for option pricing. The limitations of the Black-Scholes model and GBM in dealing with real market conditions such as stochastic volatility and jump-diffusion processes are addressed, showcasing the evolution of more complex models like the Heston model and GARCH. Interest rate models like the Vasicek and Cox-Ingersoll-Ross models are evaluated for their real-world applicability, particularly in scenarios of low and negative interest rates. This comprehensive review not only underscores the theoretical advancements in financial modeling but also its practical implications in contemporary financial markets.

Preliminary evidence for chaotic signatures in host-microbe interactions.

Host-microbe interactions constitute dynamical systems that can be represented by mathematical formulations that determine their dynamic nature and are categorized as deterministic, stochastic, or chaotic. Knowing the type of dynamical interaction is essential for understanding the system under study. Very little experimental work has been done to determine the dynamical characteristics of host-microbe interactions, and its study poses significant challenges. The most straightforward experimental outcome involves an observation of time to death upon infection. However, in measuring this outcome, the internal parameters and the dynamics of each particular host-microbe interaction in a population of interactions are hidden from the experimentalist. To investigate whether a time-to-death (time-to-event) data set provides adequate information for searching for chaotic signatures, we first determined our ability to detect chaos in simulated data sets of time-to-event measurements and successfully distinguished the time-to-event distribution of a chaotic process from a comparable stochastic one. To do so, we introduced an inversion measure to test for a chaotic signature in time-to-event distributions. Next, we searched for chaos in the time-to-death of Caenorhabditis elegans and Drosophila melanogaster infected with Pseudomonas aeruginosa or Pseudomonas entomophila, respectively. We found suggestions of chaotic signatures in both systems but caution that our results are preliminary and highlight the need for more fine-grained and larger data sets in determining dynamical characteristics. If validated, chaos in host-microbe interactions would have important implications for the occurrence and outcome of infectious diseases, the reproducibility of experiments in the field of microbial pathogenesis, and the prediction of microbial threats.IMPORTANCEIs microbial pathogenesis a predictable scientific field? At a time when we are dealing with coronavirus disease 2019, there is intense interest in knowing about the epidemic potential of other microbial threats and new emerging infectious diseases. To know whether microbial pathogenesis will ever be a predictable scientific field requires knowing whether a host-microbe interaction follows deterministic, stochastic, or chaotic dynamics. If randomness and chaos are absent from virulence, there is hope for prediction in the future regarding the outcome of microbe-host interactions. Chaotic systems are inherently unpredictable, although it is possible to generate short-term probabilistic models, as is done in applications of stochastic processes and machine learning to weather forecasting. Information on the dynamics of a system is also essential for understanding the reproducibility of experiments, a topic of great concern in the biological sciences. Our study finds preliminary evidence for chaotic dynamics in infectious diseases.

Validation of Stock Price Prediction Models in the Conditions of Financial Crisis

The distribution laws of various natural and anthropogenic processes in the world around us are stochastic in nature. The development of mathematics and, in particular, of stochastic modeling allows us to study regularities in such processes. In practice, stochastic modeling finds a huge number of applications in various fields, including finance and economics. In this work, some particular applications of stochastic processes in finance are examined in the conditions of financial crisis, aiming to provide a solid approach for stock price forecasting. More specifically, autoregressive integrated moving average (ARIMA) models and modified ordinary differential equation (ODE) models, previously developed by some of the authors to predict the asset prices of four Bulgarian companies, are validated against a time period during the crisis. Estimated rates of return are calculated from the models for one period ahead. The errors are estimated and the models are compared. The return values predicted with each of the two approaches are used to derive optimal risk portfolios based on the Markowitz model, which is the second major aim of this study. The third aim is to compare the resulting portfolios in terms of distribution (i.e., weights of the stocks), risk, and rate of return.

A Continuous-Time Markov Chain Model for the Spread of COVID-19

Summary Since late 2019 the novel coronavirus, also known as COVID-19, has caused a pandemic that persists. This paper shows how a continuous-time Markov chain model for the spread of COVID-19 can be used to explain, and justify to undergraduate students, strategies now being used in attempts to control the virus. The material in the paper is written at the level of students who are taking an introductory course on the theory and applications of stochastic processes.

Stochastic Modeling with Applications in Supply Chain Management and ICT Systems

Fast-growing technology and the development of IT services have yielded the idea of founding a new application of stochastic processes and their properties. We give a new connection between electronic process management and a relatively new stochastic process named the Non-central Polya-Aeppli process. This process is applied as a counting process in the mathematical construction of the given model, and it has been introduced as a counting process in electronic process management.

The Application of Stochastic Processes in Options Pricing Model

Since English botanist Brown first observed the inconsistent mobility of pollen floating in liquid in 1827, stochastic motion has become one of the primary research topics today, and the use of stochastic processes in financial markets has never stopped [1]. The change in the process in any time interval do not affect the change in any other time intervals that do not overlap with of Brownian Motion, which possesses stationary independent increments. Therefore, this paper obtains the Black-Scholes Merton formula from the stochastic process through layers of derivation and analyses its limitations in terms of its existence. Therefore, this paper will derive the BSM formula and the logical relationships between them, step by step, starting from the stochastic process and discuss the problems and limitations of the BSM formula. The experiential results demonstrate that the proposed method can achieve better performance.

Peculiarities and Applications of Stochastic Processes with Fractal Properties.

In this paper, the fractal properties of stochastic processes and objects in different areas were specified and investigated. These included: measuring systems and sensors, navigation and motion controls, telecommunication systems and networks, and flaw detection technologies. Additional options that occur through the use of fractality were also indicated and exemplified for each application. Regarding the problems associated with navigation information processing, the following fractal nature processes were identified: errors of inertial sensors based on the microelectromechanical systems called MEMS, in particular gyroscopic drift and accelerometer bias, and; the trajectory movement of mobile objects. With regard to navigation problems specifically, the estimation problem statement and its solution are given by way of the Bayesian approach for processing fractal processes. The modified index of self-similarity for telecommunication series was proposed, and the self-similarity of network traffic based on the R/S method and wavelet analysis was identified. In failure detection, fractality manifested as porosity, wrinkles, surface fractures, and ultrasonic echo signals measured using non-destructive sensors used for rivet compound testing.

Reliability Assessment of Repairable Systems Using Simple Regression Models

The statistical nature of failures in repairable systems does not have a behaviour similar to non-repairable systems. The statistical models developed for the study of the reliability of repairable systems mostly based on the application of stochastic processes. However, there is a group of prediction models for reliability based on time series analysis. Below are the results and conclusions of the application of simple regression models in the escalators Avante model (TNE), in order to assess their potential use by maintenance organizations.

Application of Stochastic Process in Signal Processing

In this paper introduction about birth and death Poisson process basic result of the markovian application in queuing theory used in signal processing, signal transfer from some to passion based on the intermediate node, each intermediate node are transformed from signal strength S is directly proportional to 1/√p based on the formula using the internal communication a dependent can be characterised by the Gilbert model. Two state Markov model signals, distance when signal strength is greater the distance should be reduced. Bayesian inference is used, few numerical examples are studied.

Earthquake recurrence models and occurrence probabilities of strong earthquakes in the North Aegean Trough (Greece)

The determination of strong earthquakes’ recurrence time above a predefined magnitude, associated with specific fault segments, is an important component of seismic hazard assessment. The occurrence of these earthquakes is neither periodic nor completely random but often clustered in time. This fact in connection with their limited number, due to shortage of the available catalogs, inhibits a deterministic approach for recurrence time calculation, and for this reason, application of stochastic processes is required. In this study, recurrence time determination in the area of North Aegean Trough (NAT) is developed by the application of time-dependent stochastic models, introducing an elastic rebound motivated concept for individual fault segments located in the study area. For this purpose, all the available information on strong earthquakes (historical and instrumental) with Mw ≥ 6.5 is compiled and examined for magnitude completeness. Two possible starting dates of the catalog are assumed with the same magnitude threshold, Mw ≥ 6.5 and divided into five data sets, according to a new segmentation model for the study area. Three Brownian Passage Time (BPT) models with different levels of aperiodicity are applied and evaluated with the Anderson–Darling test for each segment in both catalog data where possible. The preferable models are then used in order to estimate the occurrence probabilities of Mw ≥ 6.5 shocks on each segment of NAT for the next 10, 20, and 30 years since 01/01/2016. Uncertainties in probability calculations are also estimated using a Monte Carlo procedure. It must be mentioned that the provided results should be treated carefully because of their dependence to the initial assumptions. Such assumptions exhibit large variability and alternative means of these may return different final results.

STATISTICS OF EARTHQUAKE RECURRENCE TIME IN NORTH AEGEAN TROUGH

The determination of recurrence time of strong earthquakes of certain magnitude on a specific fault or fault segment is an important component of seismic hazard assessment. The occurrence of these earthquakes is neither periodic nor completely random but often clustered in time. This fact in connection with their limited number inhibits a deterministic approach for recurrence times calculation and thus application of stochastic processes is required. For recurrence times determination in the area of North Aegean, all the available information on strong earthquakes (historical and instrumental) with M6.0 is collected. Given that source parameters of historical events contain larger uncertainties, reassessment of their focal parameters before the application of stochastic processes is necessary, which was performed by applying the method of Bakun and Wentworth (1997). The reasses sed catalogue was divided into three data sets, according to the strong events spatial distribution and their association with distinctive fault segments. Three statistical distributions (Weibull, inverse Gaussian, lognormal) were applied and evaluated with the Anderson–Darling test and the Akaike and Bayesian Information Criteria. The Weibull distribution exhibited better performance in two out of three data sets and the Inverse Gaussian distribution in the third. With given distributions the occurrence probabilities were calculated for strong events above a certain magnitude and for certain time interval.

Poisson intensity estimation with reproducing kernels

Despite the fundamental nature of the inhomogeneous Poisson process in the theory and application of stochastic processes, and its attractive generalizations (e.g. Cox process), few tractable nonparametric modeling approaches of intensity functions exist, especially when observed points lie in a high-dimensional space. In this paper we develop a new, computationally tractable Reproducing Kernel Hilbert Space (RKHS) formulation for the inhomogeneous Poisson process. We model the square root of the intensity as an RKHS function. Whereas RKHS models used in supervised learning rely on the so-called representer theorem, the form of the inhomogeneous Poisson process likelihood means that the representer theorem does not apply. However, we prove that the representer theorem does hold in an appropriately transformed RKHS, guaranteeing that the optimization of the penalized likelihood can be cast as a tractable finite-dimensional problem. The resulting approach is simple to implement, and readily scales to high dimensions and large-scale datasets.

An application of stochastic processes for analyzing risks in highway projects

The successes on highway projects are uncertain because of organizational features, improper scope definitions and long lasting complicated processes. Highway projects under uncertain environment can effectively be managed with the application of risk management throughout their life cycles. Risk management within highway projects, therefore, has been recognized vital to improve their performances and increase the success of these projects. Processes of the projects are dynamic by nature. Therefore, commonly used static techniques do not analyze the potential risks properly. The stochastic process is a highly effective tool to quantitatively deal with the risk analysis. In this paper, a new approach based on Markov chain is proposed to assess the potential risks of highway projects in a dynamic framework. The approach takes advantage of the capability of probabilistic tools. Furthermore, using an application example in highway projects, the proposed approach is demonstrated in detail. Finally, the risk management effectiveness of using the stochastic processes is illustrated.

Applications of Stochastic Processes in Biology and Medicine

Applications of Stochastic Processes in Biology and Medicine

Contributors

Contributors

Floyd B. Hanson: Applied Stochastic Processes and Control for Jump-Diffusions

The emphasis of this monograph is on modeling and practical applications rather than on mathematical formalism. Although the level is high, the book is perfectly accessible to a wide range of readers, from graduate students to any researcher interested on modeling of stochastic processes as they arise in applied math, biology, physics, engineering and finance. The book contains 12 chapters within a bit over 400 pages. The first four chapters constitute an introduction to the subject including basic tools such as Ito calculus which is clearly explained. The rest of chapters are addressed to more advanced mathematical topics as well as a number suggested by practical applications. Thus we find stochastic calculus for general Markov processes, stochastic optimal control, Kolmogorov (i.e. Fokker-Planck) equations, stochastic simulations using Monte Carlo methods, and applications to finance (basically Black-Scholes and optimal portfolio theories) and to biology (e.g., diffusion and tumor growth). Three appendices constitute a useful addition containing some technical details such as preliminaries in probability and analysis, deterministic optimal control and MATLAB programs. These appendices are found online at the SIAM address: www.siam.org/books/dc13. The book is based on graduate courses which the author has taught during a number of years at the applied mathematics department of the University of Illinois at Chicago. I believe that the book will be appealing and useful to students as well as researchers interested on applications of stochastic processes.

The Computer Control System and Algorithm for Plate Mill

Since 1988, We have made computer control reforming of hydraulic screwdown in five plate mills, and have achieved a series of satisfied system performance such as rapid response, the two side of rolls to move synchronistically, anti-interference etc., we also gained high—accuracy plate thickness. The statistics thickness variations within one plate are in range of 0.25 – 0.60 mm before reforming and are less than 0.03 – 0.15 mm after reforming. The errors of hitting aimed thickness less than ± 0.10 mm, The extreme variations of batch less than 0.07 mm. The techniques of reforming are mainly dynamic intelligent control of hydraulic screwdown system, synchronism control of hydraulic screwdown, eccentricity control method by rotary encoder, the curve of modulus of mill measured automatically, the control algorithm of reducing the variation within one plate, the hitting aimed thickness of plates and the application of stochastic process in AGC system etc. The techniques was fully and successfully industrialized to The Plate Mill of MaAnshan Iron & Steel Co. LTD and Steel Sheet Plant of Shanghai No.1 Iron & Steel Works.

Engineering Applications of Stochastic Processes

(1991). Engineering Applications of Stochastic Processes. Technometrics: Vol. 33, No. 1, pp. 120-120.

The music machine: Selected readings from ?computer music journal?

Computer applications to music cover a very large field. This book is a collection of articles, previously published in Computer Music Journal, one of the most respected journals in the field, which deal with some of the possible applications of automated tools in music. The book, edited by the one-time editor of the journal, consists of 54 contributions divided into eight chapters: “Interviews,” “Composition,” “The Midi Interface,” “Music Software,” “Synthesis and Signal Processing,” “ Signal Processing Hardware” and “Music and Artificial Intelligence.” In the first chapter, computer musicians are interviewed on their experience of using computers to produce sound or musical compositions and in the second, several composers describe their compositional experiments. The next four chapters focus on both hardware and software developments, mainly to process signals or to manipulate musical data. A few treat music printing or applications of stochastic processes to music or describe commercial packages. The last chapter, on AI and music, is surely the most interesting for people working in computational linguistics because it concerns problems, like formalizing knowledge, theory testing and so on, which linguistics and music share. The short but very interesting article by John Rothgeb, “Simulating Musical Skills by Digital Computer,” focuses on the use of the computer to analyze what the theories of unfigured bass lack. He implemented rules extracted from theoretical attempts to harmonize the bass part, but the resulting failures demonstrated the lack of explanatory power of the theory. Therefore, the computer can be used to investigate musical theories by implementing them and then redefining or improving them by studying the results obtained from observation of how the implementations work out. Another essay of interest in this chapter is John Rahn’s “On Some Computational Models of Music Theory” in which some theoretical and practical issues raised by other authors are discussed and criticized. Of interest from the computational linguist’s point of view would be the discussion and criticism of the possible relationship, proposed by Meehan (1980), between Schank’s Conceptual Dependency Theory and the theory of implication/realization worked

Book Review: Modelling and Application of Stochastic Processes

Book Review: Modelling and Application of Stochastic Processes