66 Results Found

In this paper, quantitative mean square exponential stability and stabilization of Itô-type linear stochastic Markovian jump systems with Brownian and Poisson noises are investigated. First, the definition of quantitative mean square exponentia...

The classical problem of stabilization of the controlled inverted pendulum is considered in the case of stochastic perturbations of the type of Poisson’s jumps. It is supposed that stabilized control depends on the entire trajectory of the pend...

The stochastic linear–quadratic optimal control problem with Poisson jumps is addressed in this paper. The coefficients in the state equation and the weighting matrices in the cost functional are all deterministic but are allowed to be indefini...

In this paper, we study the averaging principle for $\psi$-Capuo fractional stochastic delay differential equations (FSDDEs) with Poisson jumps. Based on fractional calculus, Burkholder-Davis-Gundy’s inequality, Doob’s martingale inequalit...

The stability analysis of the numerical solutions of stochastic models has gained great interest, but there is not much research about the stability of stochastic pantograph differential equations. This paper deals with the almost sure exponential st...

The existence of mild solutions and the approximate controllability for a class of Sobolev-type $\psi$-Caputo fractional stochastic evolution equations (SCFSEEs) subject to nonlocal conditions and Poisson jumps are investigated in this paper. First, t...

In this paper, we investigate the optimal control problems for a class of neutral stochastic integrodifferential equations (NSIDEs) with infinite delay driven by Poisson jumps and the Rosenblat process in Hilbert space involving concrete-fading memor...

First-exit problems are studied for two-dimensional diffusion processes with jumps according to a Poisson process. The size of the jumps is distributed as an exponential random variable. We are interested in the random variable that denotes the first...

This study considers a class of backward stochastic semi-linear Schrödinger equations with Poisson jumps in ${\mathbb{R}}^d$ or in its bounded domain of a $C^2$ boundary, which is associated with a stochastic control problem of nonlinear Schrödinger equatio...

This work investigates fractional stochastic Schrödinger evolution equations in a Hilbert space, incorporating complex potential symmetry and Poisson jumps. We establish the existence of mild solutions via stochastic analysis, semigroup theory,...

In this manuscript, a new class of impulsive fractional Caputo neutral stochastic differential equations with variable delay (IFNSDEs, in short) perturbed by fractional Brownain motion (fBm) and Poisson jumps was studied. We utilized the Carath&eacut...

In this paper, a class of time-space fractional stochastic delay control problems with fractional noises and Poisson jumps in a bounded domain is considered. The proper function spaces and assumptions are proposed to discuss the existence of mild sol...

The aim of this article is to consider a class of neutral Caputo fractional stochastic evolution equations with infinite delay (INFSEEs) driven by fractional Brownian motion (fBm) and Poisson jumps in Hilbert space. First, we establish the local and...

The truncated Euler–Maruyama (EM) method for stochastic differential equations with Poisson jumps (SDEwPJs) has been proposed by Deng et al. in 2019. Although the finite-time $L^r$-convergence theory has been established, the strong convergence th...

The paper presents a new mathematical model of TCP (Transmission Control Protocol) link functioning in a heterogeneous (wired/wireless) channel. It represents a controllable, partially observable stochastic dynamic system. The system state describes...

In traditional finance, option prices are typically calculated using crisp sets of variables. However, as reported in the literature novel, these parameters possess a degree of fuzziness or uncertainty. This allows participants to estimate option pri...

In this paper, we explore the stability of a new class of Caputo-type fractional stochastic delay differential systems with Poisson jumps. We prove the Hyers–Ulam stability of the solution by utilizing a version of fixed point theorem, fraction...

In this paper, we obtain the existence and uniqueness theorem for solutions of Caputo-type fractional stochastic delay differential systems(FSDDSs) with Poisson jumps by utilizing the delayed perturbation of the Mittag–Leffler function. Moreove...

This paper investigates a new class of fractional stochastic differential systems with non-Gaussian processes and Poisson jumps. Firstly, we examine the solvability results for the considered system. Furthermore, new stability results for the propose...

We introduce the conformable fractional (CF) noninstantaneous impulsive stochastic evolution equations with fractional Brownian motion (fBm) and Poisson jumps. The approximate controllability for the considered problem was investigated. Principles an...

We deal with a multidimensional Markovian backward stochastic differential equation driven by a Poisson random measure and independent Brownian motion (BSDEJ for short). As a first result, we prove, under the Lipschitz condition, that the BSDEJ&rsquo...

In this paper, we focus on investigating the well-posedness of backward stochastic differential equations with jumps (BSDEJs) driven by irregular coefficients. We establish new results regarding the existence and uniqueness of solutions for a specifi...

We focus on solving stochastic differential equations driven by jump processes (SDEJs) with measurable drifts that may exhibit quadratic growth. Our approach leverages a space transformation and Itô-Krylov’s formula to effectively elimina...

Each charging/discharging cycle leads to a gradual decrease in the battery’s capacity. The degradation of capacity in lithium-ion batteries represents a non-monotonous process with random jumps. Earlier studies claimed that the instantaneous de...

This paper proposes a new fractional Poisson process through a recursive fractional differential governing equation. Unlike the homogeneous Poison process, the Caputo derivative on the probability distribution of k jumps with respect to time is linke...

This paper extends the traditional jump-diffusion model to a comprehensive general Lévy process model with the stochastic interest rate for European-style options pricing. By using the Girsanov theorem and Itô formula, we derive the unif...

The current paper is devoted to the dynamical property of the stochastic Cox–Ingersoll–Ross (CIR) model with pure jump noise, which is an extension of the CIR model. Firstly, we characterize the existence and 2-moment of the CIR process w...

In this paper, we consider the Wiener–Poisson risk model, which consists of a Wiener process and a compound Poisson process. Given the discrete record of observations, we use a threshold method and a regularized Laplace inversion technique to e...

Filtered Poisson processes are used as models in various applications, in particular in statistical hydrology. In this paper, controlled filtered Poisson processes are considered. The aim is to minimize the expected time that the process will spend i...

We propose a parameter estimation method for non-stationary Poisson time series with the abnormal fluctuation scaling, known as Taylor’s law. By introducing the effect of Taylor’s fluctuation scaling into the State Space Model with the Pa...

Energy commodities and their futures naturally show cointegrated price movements. However, there is empirical evidence that the prices of futures with different maturities might have, e.g., different jump behaviours in different market situations. Ob...

A fluctuation theory and, in particular, a theory of scale functions is developed for upwards skip-free Lévy chains, i.e., for right-continuous random walks embedded into continuous time as compound Poisson processes. This is done by analogy t...

This paper continues a series of papers by the author devoted to unsolved problems in the theory of stability and optimal control for stochastic systems. A delay differential equation with stochastic perturbations of the white noise and Poisson&rsquo...

Auxetic materials have a negative Poisson’s ratio, meaning they contract laterally during axial compression. Auxetics can also absorb more energy during impacts than conventional materials. Auxetic foam was fabricated by volumetrically compress...

In this study, we explore backward stochastic differential equations driven by a Poisson process and an independent Brownian motion, denoted for short as BSDEJs. The generator exhibits logarithmic growth in both the state variable and the Brownian co...

This paper is aimed at developing a stochastic volatility model that is useful to explain the dynamics of the returns of gold, silver, and platinum during the period 1994–2019. To this end, it is assumed that the precious metal returns are driven by...

In this paper, we study the indefinite linear-quadratic (LQ) stochastic optimal control problem for stochastic differential equations (SDEs) with jump diffusions and random coefficients driven by both the Brownian motion and the (compensated) Poisson...

Dong, Goldschmidt and Martin (2006) (DGM) showed that, for $0<\alpha <1,$ and $\theta >-\alpha$, the repeated application of independent single-block fragmentation operators based on mass partitions following a two-parameter Poisson&ndash...

At present, it is customary to consider the overlimit operating modes of electromembrane systems to be effective, and electroconvection as the main mechanism of overlimiting transfer. The breakdown of the space charge is a negative, “destructiv...

A new high-order hybrid method integrating neural networks and corrected finite differences is developed for solving elliptic equations with irregular interfaces and discontinuous solutions. Standard fourth-order finite difference discretization beco...

We study a hybrid stochastic SIS co-infection model for two primary strains and a co-infected class with Crowley–Martin incidence, Markovian regime switching, and Lévy jumps. The model is a four-dimensional regime-switching Lévy-d...

This paper considers the optimal investment problem in a financial market with one risk-free asset and one jump-diffusion risky asset. It is assumed that the insurance risk process is driven by a compound Poisson process and the two jump number proce...

An optimal control for a dynamical system optimizes a certain objective function. Here, we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps, which makes...

In this paper, an accurate distribution of stress as well as corresponding factors of stress concentration determination around a spherical cavity, which is considered as embedded in a cylinder exposed to the internal pressure only, is presented. Thi...

We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connections with b...

This article proposes a 3D mathematical model of the influence of electrical heterogeneity of the ion exchange membrane surface on the processes of salt ion transfer in membrane systems with axial symmetry; in particular, we investigate an annular me...

This paper considers the valuation of a vulnerable option when underlying stock is subject to liquidity risks. That is, it is assumed that the underlying stock is not perfectly liquid. We establish a framework where the stock price follows the stocha...

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 non...

In this study, we investigate the mixed n-layer ratcheting dividend and capital injection policies for a spectrally negative Lévy risk model, where dividend distributions are implemented continuously in a non-decreasing manner, and capital inj...

A mean-field linear quadratic stochastic (MF-SLQ for short) optimal control problem with hybrid disturbances and cross terms in a finite horizon is concerned. The state equation is a systems driven by the Wiener process and the Poisson random marting...