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Journal of Control and Decision 2023年第4期10卷 538-546页

作者： K.Ramkumar K.Ravikumar E.M.Elsayed Department of Mathematics with CA PSG College of Arts&ScienceCoimbatoreIndia Department of Mathematics PSG College of Arts&ScienceCoimbatoreIndia Department of Mathematics Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia Department of Mathematics Faculty of ScienceMansoura UniversityMansouraEgypt

In this work,the optimal control for a class of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and poisson jumps has been discussed in infinite dimensional space involving the Hilfer fractional ***,we study the existence and uniqueness of mild solution results are proved by the virtue of fractional calculus,successive approximation method and stochastic analysis ***,the optimal control of the proposed problem is presented by using Balder’s ***,an example is demonstrated to illustrate the obtained theoretical results.

关键词： Hilfer fractional derivative stochastic integrodifferential systems Rosenblatt process poisson jumps successive approximation optimal control

Approximate Controllability of Second-Order Neutral Stochastic Differential Equations with Infinite Delay and poisson jumps

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Journal of Systems Science & Complexity 2015年第5期28卷 1033-1048页

作者： PALANISAMY Muthukumar CHINNATHAMBI Rajivganthi Department of Mathematics Gandhigram Rural Institute-Deemed University

The modelling of risky asset by stochastic processes with continuous paths, based on Brownian motions, suffers from several defects. First, the path continuity assumption does not seem reasonable in view of the possibility of sudden price variations(jumps) resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the poisson random measure. Many popular economic and financial models described by stochastic differential equations with poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.

关键词： Approximate controllability Hilbert space poisson jumps second-order neutral stochastic differential equations semigroup theory

Strong convergence rate of truncated Euler-Maruyama method for stochastic differential delay equations with poisson jumps

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Frontiers of Mathematics in China 2021年第2期16卷 395-423页

作者： Shuaibin GAO Junhao HU Li TAN Chenggui YUAN School of Mathematics and Statistics South-Central University for NationalitiesWuhan 430074China School of Statistics Jiangxi University of Finance and EconomicsNanchang 330013China Research Center of Applied Statistics Jiangxi University of Finance and EconomicsNanchang 330013China Department of Mathematics Swansea UniversitySwanseaSA28PPUK

We study a class of super-linear stochastic differential delay equations with poisson jumps (SDDEwPJs). The convergence and rate of the convergence of the truncated Euler-Maruyama numerical solutions to SDDEwPJs are i... 详细信息

关键词： Truncated Euler-Maruyama method stochastic differential delay equations poisson jumps rate of the convergence

Approximate Controllability of Second-Order Neutral Stochastic Differential Equations with Infinite Delay and poisson jumps

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Journal of Systems Engineering and Electronics 2015年第5期26卷 1033-1048页

作者： PALANISAMY Muthukumar CHINNATHAMBI Rajivganthi Department of Mathematics Gandhigram Rural Institute-Deemed University

The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations （jumps） resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the poisson random measure. Many popular economic and financial models described by stochastic differential equations with poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.

关键词： Approximate controllability Hilbert space poisson jumps second-order neutral stochas-tic differential equations semigroup theory.

Global Attracting Sets of Neutral Stochastic Functional Differential Equations Driven by poisson jumps

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Journal of Partial Differential Equations 2021年第2期34卷 103-115页

作者： XIE Qiaoqiao YANG Bin LI Zhi College of Education and Sports Sciences Yangtze UniversityJingzhou 434023China School of Information and Mathematics Yangtze UniversityJingzhou 434023China

By means of the Banach fixed point principle,we establish some sufficient conditions ensuring the existence of the global attracting sets and the exponential decay in the mean square of mild solutions for a class of neutral stochastic functional differential equations by poisson *** example is presented to illustrate the effectiveness of the obtained result.

关键词： Global attracting set mild solution Banach fixed point principle poisson jumps

Freidlin-Wentzell’s Large Deviations for Stochastic Evolution Equations with poisson jumps

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Advances in Pure Mathematics 2016年第10期6卷 676-694页

作者： Huiyan Zhao Siyan Xu School of Economics and Statistics Guangzhou University Guangzhou China School of Applied Mathematics Beijing Normal University Zhuhai Zhuhai China Faculty of Science Ningbo University Ningbo China

We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with poisson jumps and small multiplicative noises by using weak convergence method.

关键词： Stochastic Evolution Equation poisson jumps Freidlin-Wentzell’s Large Deviation Weak Convergence Method

THE TRUNCATED EM METHOD FOR JUMP-DIFFUSION SDDES WITH SUPER-LINEARLY GROWING DIFFUSION AND JUMP COEFFICIENTS

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Journal of Computational Mathematics 2024年第1期42卷 178-216页

作者： Shounian Deng Chen Fei Weiyin Fei Xuerong Mao Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment Ministry of Educationand School of Mathematics-Physics and FinanceAnhui Polytechnic UniversityWuhu 241000China Business School University of Shanghai for Science and TechnologyShanghai 200093China Department of Mathematics and Statistics University of StrathclydeGlasgow G11XHUK

This work is concerned with the convergence and stability of the truncated EulerMaruyama(EM)method for super-linear stochastic differential delay equations(SDDEs)with time-variable delay and poisson *** constructing appropriate truncated functions to control the super-linear growth of the original coefficients,we present two types of the truncated EM method for such jump-diffusion SDDEs with time-variable delay,which is proposed to be approximated by the value taken at the nearest grid points on the left of the delayed *** first type is proved to have a strong convergence order which is arbitrarily close to 1/2 in mean-square sense,under the Khasminskii-type,global monotonicity with U function and polynomial growth *** second type is convergent in q-th(q<2)moment under the local Lipschitz plus generalized Khasminskii-type *** addition,we show that the partially truncated EM method preserves the mean-square and H∞stabilities of the true ***,we carry out some numerical experiments to support the theoretical results.

关键词： SDDEs Truncated EM method Time-variable delay poisson jumps

STRONG CONVERGENCE OF JUMP-ADAPTED IMPLICIT MILSTEIN METHOD FOR A CLASS OF NONLINEAR JUMP-DIFFUSION PROBLEMS

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Journal of Computational Mathematics 2024年第1期42卷 248-270页

作者： Xu Yang Weidong Zhao School of Mathematics China University of Mining and TechnologyXuzhou 221116China School of Mathematics Shandong UniversityJinan 250100China

In this paper,we study the strong convergence of a jump-adapted implicit Milstein method for a class of jump-diffusion stochastic differential equations with non-globally Lipschitz drift *** with the regular methods,the jump-adapted methods can significantly reduce the complexity of higher order methods,which makes them easily implementable for scenario ***,due to the fact that jump-adapted time discretization is path dependent and the stepsize is not uniform,this makes the numerical analysis of jump-adapted methods much more involved,especially in the non-globally Lipschitz *** provide a rigorous strong convergence analysis of the considered jump-adapted implicit Milstein method by developing some novel analysis techniques and optimal rate with order one is also successfully *** experiments are carried out to verify the theoretical findings.

关键词： Jump-diffusion Jump-adapted implicit Milstein method poisson jumps Strong convergence rate Non-Lipschitz coefficients

Mean-square Stability of Stochastic Age-dependent Delay Population Systems with jumps

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Acta Mathematicae Applicatae Sinica 2018年第1期34卷 145-154页

作者： Qiang LI Qi-min ZHANG Bo-qiang CAO School of Mathematics and Statistics Ningxia University Yinchuan 750021 China School of Mathematics and Information Sciences Beifang University of Nationalities Yinchuan 750021 China

In this paper, we present the compensated stochastic θ method for stochastic age-dependent delay population systems（SADDPSs） with poisson jumps. The definition of mean-square stability of the numerical solution is given and a sufficient condition for mean-square stability of the numerical solution is derived. It is shown that the compensated stochastic θ method inherits stability property of the numerical solutions. Finally,the theoretical results are also confirmed by a numerical experiment.

关键词： stochastic age-dependent delay population systems compensated stochastic θ method poisson jumps mean-square stability

The Stability of Jump-Diffusion Model

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The Stability of Jump-Diffusion Model