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Journal of Systems Science & Complexity 2020年第6期33卷 1886-1902页

作者： XU Xiaoming Institute of Finance and Statistics School of Mathematical SciencesNanjing Normal UniversityNanjing210023China

This paper considers the fully coupled forward-backward stochastic functional differential equations(FBSFDEs) with stochastic functional differential equations as the forward equations and the generalized anticipated backward stochastic differential equations as the backward equations. The authors will prove the existence and uniqueness theorem for FBSFDEs. As an application, we deal with a quadratic optimal control problem for functional stochastic systems, and get the explicit form of the optimal control by virtue of FBSFDEs.

关键词： Forward-backward stochastic functional differential equation functional stochastic system generalized anticipated backward stochastic differential equation quadratic optimal control stochastic functional differential equation

ASYMPTOTIC STABILITIES OF stochastic functional differential equationS

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Applied Mathematics and Mechanics(English Edition) 2006年第11期27卷 1577-1584页

作者：沈轶江明辉廖晓昕 Department of Control Science and Engineering Huazhong University of Science and TechnologyWuhan 430074P. R. China

Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of the solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in application, were obtained, The results show that the wellknown classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify our results.

关键词： stochastic functional differential equation stochastic neural network asymptotic stability semi-martingale convergence theorem Ito^ formula

Non-densely defined impulsive neutral stochastic functional differential equations driven by fBm in Hilbert space with infinite delay

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Frontiers of Mathematics in China 2015年第2期10卷 351-365页

作者： Yong REN Tingting HOU R. SAKTHIVEL Department of Mathematics Anhui Normal University Wuhu 241000 China Department of Mathematics Sungkyunkwan University Suwon 440-746 Korea

We study a class of non-densely defined impulsive neutral stochastic functional differential equations driven by an independent cylindrical fractional Brownian motion （fBm） with Hurst parameter H ∈ （1/2, 1） in the Hilbert space. We prove the existence and uniqueness of the integral solution for this kind of equations with the coefficients satisfying some non-Lipschitz conditions. The results are obtained by using the method of successive approximation.

关键词： stochastic functional differential equation non-densely defined operator cylindrical fractional Brownian motion (fBm) impulsive effect

Global Solutions and Exponential Stability of stochastic functional differential equations with Infinite Delay

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Journal of Southwest Jiaotong University(English Edition) 2010年第1期18卷 85-90页

作者：徐勇胡适耕 Department of Mathematics Huazhong University of Science and Technology

This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment ... 详细信息

关键词： stochastic functional differential equation Infinite delay Global solution Moment exponential stability

STABILITY OF THE SOLUTIONS TO stochastic functional differential equationS WITH INFINITE DELAY

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Annals of differential equations 2009年第2期25卷 219-222页

作者： Chaohui Yue1,2,Lianglong Wang1 (1. School of Math. Sciences,Anhui University,Hefei 230039 2. School of Sciences,Anhui Agricultural University,Hefei 230036) School of Math. Sciences Anhui University Hefei 230039 School of Sciences Anhui Agricultural University Hefei 230036 School of Math. Sciences Anhui University Hefei 230039

In this paper,we obtain the stability of solutions to stochastic functional differential equations with infinite delay at phase space BC((-∞,0];Rd),under non-Lipschitz condition with Lipschitz condition being conside... 详细信息

关键词： stochastic functional differential equation infinite delay

European Option Pricing with Time Delay

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European Option Pricing with Time Delay