Jump Process Research Articles (Page 1)

In ski jumping, studying to determine a reasonable run-up posture can effectively reduce air resistance during the run-up phase, thereby increasing sliding speed. However, most current research focuses on kinematic analysis from video perspectives, with fewer studies examining dynamics. Therefore, this paper proposes a maximum speed take-off model based on particle swarm optimization and ODE solver from a dynamic perspective. First, a dynamic model is established using Newtonian mechanics principles, incorporating dynamic factors for attitude control and determining relevant initial parameters. Then, the sliding process is simulated using an ODE solver, and the optimal attitude control parameters are determined using particle swarm optimization. The final model concludes that squatting during the run-up significantly reduces resistance and increases take-off speed. By further considering aerodynamic effects and refining the model by introducing real-time dynamic data, this model can become a core tool for training in winter sports research.

Abstract The study of consensus in multiagent systems (MASs) serves as a critical foundation for the development of smart cities, enabling coordinated and efficient operation of distributed agents. This paper focuses on MASs where agents operate in different modes with a hierarchical semi‐Markov jumping process. The state transitions of the system are governed by a jumping signal, which offers a general and realistic representation of dynamic systems, enhancing its applicability to practical scenarios. In addition, the potential for communication network vulnerabilities is considered such as deception attacks. To address these challenges, a resilient consensus controller is designed, capable of mitigating the effects of deception attacks characterized by a Bernoulli probability distribution. To achieve leader–follower consensus in the mean‐square sense, mathematical techniques, including linear matrix inequalities (LMIs) and matrix decomposition, are employed. These methods help derive sufficient conditions for system consensus and facilitate the design of the resilient controller simultaneously. Finally, numerical simulations verify the effectiveness of the proposed approach, highlighting its ability to maintain system stability and performance under varying operational modes and potential attacks.

Abstract The notion of Markov duality between two Markov processes that can live in two different configurations spaces ( x , x ~ ) is revisited via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right and left eigenvectors. In this formulation, the two generators should have the same eigenvalues ( − E ) that may be complex, while the duality function Ω ( x , x ~ ) can be considered as a mapping between the right and the left eigenvectors of the two models. We describe how this spectral perspective is useful to better understand two well-known dualities between processes defined in the same configuration space: the Time-Reversal duality corresponds to an exchange between the right and the left eigenvectors that involves the steady state, while in the Siegmund duality, the left eigenvectors correspond to integrals of the dual right eigenvectors. We then focus on the famous Moment-Duality between the Wright–Fisher diffusion on the interval x ∈ [ 0 , 1 ] and the Kingman Markov jump process on the semi-infinite lattice n ∈ N in order to analyze the relations between their eigenvectors living in two different configuration spaces. Finally, we discuss how the spectral perspective can be used to construct new dualities and we give an example for the case of non-degenerate real eigenvalues, where one can always construct a dual Directed Jump process on the semi-infinite lattice n ∈ N , whose transitions rates are the opposite-eigenvalues.

This article investigates the zonotope-based state estimation for boost converter system with Markov jump process. DC-DC boost converters are pivotal in modern power electronics, enabling renewable energy integration, electric vehicle charging, and microgrid operations by elevating low input voltages from sources like photovoltaics to stable high outputs. However, their nonlinear dynamics and sensitivity to uncertainties/disturbances degrade control precision, driving research into robust state estimation. To address these challenges, the boost converter is modeled as a Markov jump system to characterize stochastic switching, with time delays, disturbances, and noises integrated for a generalized discrete-time model. An adaptive event-triggered mechanism is adopted to administrate the data transmission to conserve communication resources. A zonotopic set-membership estimation design is proposed, which involves designing an observer for the augmented system to ensure performance and developing an algorithm to construct zonotopes that enclose all system states. Finally, numerical simulations are performed to verify the effectiveness of the proposed approach.

This article proposes a new nonparametric test for detecting short-lived locally explosive trends (drift bursts) in pure-jump processes. The new test is designed specifically to detect intraday flash crashes and gradual jumps in cryptocurrency prices recorded at a high frequency. Empirical analysis shows that drift bursts in bitcoin price occur, on average, every second day. Their economic importance is highlighted by showing that hedge funds holding cryptocurrency in their portfolios are exposed to a risk factor associated with the intensity of bitcoin crashes. On average, hedge funds do not profit from intraday bitcoin crashes and do not hedge against the associated risk.

This study proposes a novel hybrid framework that integrates a jump model with model predictive control (JM-MPC) for dynamic asset allocation under regime-switching market conditions. The proposed approach leverages the jump model to identify distinct market regimes while incorporating a rolling prediction mechanism to estimate time-varying asset returns and covariance matrices across multiple horizons. These regime-dependent estimates are subsequently used as inputs for an MPC-based optimization process to determine optimal asset allocations. Through comprehensive empirical analysis, we demonstrate that the JM-MPC framework consistently outperforms an equal-weighted portfolio, delivering superior risk-adjusted returns while substantially mitigating portfolio drawdowns during high-volatility periods. Our findings establish the effectiveness of combining regime-switching modeling with model predictive control techniques for robust portfolio management in dynamic financial markets.

In this study, an improved jump model is proposed for the Roesser-type 2-D Markov jump systems (MJSs). We use two independent Markov chains that propagate along the horizontal and vertical directions, respectively, to characterize the switching of system dynamics in those two directions. Compared with the conventional jump model, which uses only one Markov chain to characterize the switching of system dynamics in both directions, the newly proposed 2-D jump model shows better modeling capabilities for real-world applications with abrupt changes while inherently avoiding the mode ambiguity phenomenon. Based on the proposed jump model, we then propose a dual-mode-dependent state feedback control law to stabilize the concerned 2-D MJS. A sufficient criterion, whose feasibility is enhanced via a dual-mode-dependent Lyapunov functional technique, is obtained to ensure the asymptotic mean square stability and H∞ disturbance attenuation level of the resulting closed-loop system. Subsequently, resorting to a novel nonconservative separation principle, two equivalent conditions with one of them in the form of linear matrix inequalities (LMIs) are developed. Finally, a convex optimization algorithm which is formulated by the obtained LMIs is proposed to design the control law. An example of the Darboux equation with Markov switching parameters is presented to validate the effectiveness of the obtained results.

The effective reproduction number is an important descriptor of an infectious disease epidemic. In small populations, ideally we would estimate the effective reproduction number using a Markov Jump Process (MJP) model of the spread of infectious disease, but in practice this is computationally challenging. We propose a computationally tractable approximation to an MJP which tracks only latent and infectious individuals, the EI model, an MJP where the time-varying immigration rate into the E compartment is equal to the product of the proportion of susceptibles in the population and the transmission rate. We use an analogue of the central limit theorem for MJPs to approximate transition densities as normal, which makes Bayesian computation tractable. Using simulated pathogen RNA concentrations collected from wastewater data, we demonstrate the advantages of our stochastic model over its deterministic counterpart for the purpose of estimating effective reproduction number dynamics, and compare against a state of the art method. We apply our new model to inference of changes in the effective reproduction number of SARS-CoV-2 in several college campus communities that were put under wastewater pathogen surveillance in 2022.

Erratum to: “Stochastic Reaction-diffusion Equations Driven by Jump Processes”

The Article Abstract is not Available.

A Quantum Jump Model of Option Pricing

An Efficient Numerical Method for Pricing Options Under Stochastic Volatility with Jump Model

Jump processes in stable stochastic differential equations (SDEs) with jumps disrupt their stable state, leading to large fluctuations that hinder parameter estimation. Regularization methods alone are often insufficient to handle the large fluctuations during non-stationary phases of SDEs. This paper proposes a more robust estimation method for SDEs with jumps by smoothing the impact of jump disturbances in the data. The proposed method utilizes quadratic variation to detect the starting points when the stable stochastic process enters a stable state and the recovery points from jump shocks. Based on this detection, a novel OU bridge replacement for regularized parameter estimation is employed to smooth out the jump disturbance segments in the original data. Repeated experimental results demonstrate that these smoothing techniques can enhance the accuracy of parameter estimation for stable SDEs with jumps. We expect these methods to contribute to improved analysis of financial historical data.

Sustainable cryptocurrency modeling is vital for maximizing both economic and environmental benefits amid significant investor interest. This research develops a comprehensive methodology for cryptocurrency selection by holistically integrating financial aspects, such as returns and risk, with environmental sustainability. To quantify risk and further evaluate cryptocurrency efficiency, we employ an ARMA-GARCH model with fractional normal inverse Gaussian (FNIG) innovations to forecast Value at Risk (VaR) and expected returns. Subsequently, we apply Data Envelopment Analysis (DEA) to identify the most efficient cryptocurrencies, incorporating mining costs and the forecasted VaR as inputs—representing energy cost and risk, respectively—while using the forecasted expected returns as the output. This approach enables a direct comparison of cryptocurrencies based on these critical factors. Our findings demonstrate that accounting for the inherent stochastic behavior of cryptocurrencies leads to more accurate estimations, and the DEA highlights the essential role of energy costs in selecting efficient cryptocurrencies.

The phenomenon of coalescence-induced droplet jumping on superhydrophobic surfaces has broad application prospects in a variety of engineering applications, including enhancement of condensation heat transfer, energy harvesting, anti-icing, and self-cleaning. Therefore, it has attracted in-depth attention and research from numerous scholars. Numerous studies have demonstrated that the structural effect can markedly increase the jumping velocity; however, there is a relative paucity of research examining the influence of energy conversion on droplet dynamics during the jumping process, and the mechanisms underlying the enhancement of jumping velocity remain to be fully elucidated. This paper investigates the droplet dynamics on superhydrophobic triangular prisms using the lattice Boltzmann method. The study reveals that the upward driving force, jointly induced by surface tension, the superhydrophobic surface, and the triangular prism structure, is a critical factor in enhancing droplet jumping. As the apex angle decreases and the length and height increase, the droplet jumping velocity generally tends to rise. Furthermore, the structural parameters related to triangular prism selectively influence different stages of the coalescence-induced droplet jumping. Notably, the energy conversion rate on the superhydrophobic triangular prism significantly increases to 16%, compared to a rate of η≤6% on a flat surface. This research seeks to give theoretical proposals for the optimization of microstructures on superhydrophobic surfaces in relevant fields, potentially guiding future advancements and applications.

H2 dynamic output feedback control of phase-type semi-Markov jump linear systems

Entomopathogenic nematodes (EPNs) exhibit a bending-elastic instability, or kink, before becoming airborne, a feature previously hypothesized but not substantiated to enhance jumping performance. Here, we provide the evidence that this kink is crucial for improving launch performance. We demonstrate that EPNs actively modulate their aspect ratio, forming a liquid-latched α-shaped loop over a slow timescale [Formula: see text] (1 second), and then rapidly open it [Formula: see text] (10 microseconds), achieving heights of 20 body lengths and generating power of ∼104 watts per kilogram. Using a bioinspired physical model [termed the soft jumping model (SoftJM)], we explored the mechanisms and implications of this kink. EPNs control their takeoff direction by adjusting their head position and center of mass, a mechanism verified through phase maps of jump directions in numerical simulations and SoftJM experiments. Our findings reveal that the reversible kink instability at the point of highest curvature on the ventral side enhances energy storage using the nematode's limited muscular force. We investigated the effect of the aspect ratio on kink instability and jumping performance using SoftJM and quantified EPN cuticle stiffness with atomic force microscopy measurements, comparing these findings with those of Caenorhabditis elegans. This investigation led to a stiffness-modified SoftJM design with a carbon fiber backbone, achieving jumps of ∼25 body lengths. Our study reveals how harnessing kink instabilities, a typical failure mode, enables bidirectional jumping in soft robots on complex substrates like sand, offering an approach for designing limbless robots for controlled jumping, locomotion, and even planetary exploration.

FILTERING OF STATES AND PARAMETERS OF SPECIAL MARKOV JUMP PROCESSES VIA INDIRECT PERFECT OBSERVATIONS

Abstract The safety valve is an automatically opening valve commonly used in pressure equipment. When the medium pressure exceeds the design pressure, the safety valve will automatically trip to protect the pressure equipment. The working state of a safety valve is related to the physical properties of the medium it carries, especially the temperature of the medium and the fluid jet at the moment of opening the safety valve. This article uses fluid structure coupling to analyse the velocity field of the safety valve nozzle and the density and medium field to provide the changes in pressure and spring force during the safety valve jumping process, providing theoretical guidance for the revision of the set pressure value for low-temperature safety valve calibration.

Jump-diffusion algorithms are applied to sampling from Bayesian posterior distributions. We consider a class of random sampling algorithms based on continuous-time jump processes. The semigroup theory of random processes lets us show that limiting cases of certain jump processes acting on discretized spaces converge to diffusion processes as the discretization is refined. One of these processes leads to the familiar Langevin diffusion equation; another leads to an entirely new diffusion equation.