Existence, uniqueness and almost surely asymptotic estimations of the solutions to neutral stochastic functional differential equations driven by pure jumps

被引：30

作者：

Mao, Wei ^{[1
]}

Zhu, Quanxin ^{[2
,3
]}

Mao, Xuerong ^{[4
]}

机构：

[1] Jiangsu Second Normal Univ, Sch Math & Informat Technol, Nanjing 210013, Jiangsu, Peoples R China

[2] Nanjing Normal Univ, Sch Math Sci, Nanjing 210023, Jiangsu, Peoples R China

[3] Nanjing Normal Univ, Inst Finance & Stat, Nanjing 210023, Jiangsu, Peoples R China

[4] Univ Strathclyde, Dept Math & Stat, Glasgow G1 1XH, Lanark, Scotland

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2015年 / 254卷

基金：

中国国家自然科学基金;

关键词：

Neutral stochastic functional differential equations; Pure jumps; Existence and uniqueness; Exponential estimations; Almost surely asymptotic estimations; RAZUMIKHIN-TYPE THEOREMS; EXPONENTIAL STABILITY; DELAY EQUATIONS; APPROXIMATIONS;

D O I：

10.1016/j.amc.2014.12.126

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are concerned with neutral stochastic functional differential equations driven by pure jumps (NSFDEwPJs). We prove the existence and uniqueness of the solution to NSFDEwPJs whose coefficients satisfying the local Lipschitz condition. In addition, we establish the p-th exponential estimations and almost surely asymptotic estimations of the solution for NSFDEwJs. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：252 / 265

页数：14

共 23 条

[1]

Applebaum D., 2004, Levy Processes and Stochastic Calculus

[2] ON THE ALMOST SURE RUNNING MAXIMA OF SOLUTIONS OF AFFINE STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS [J].

Appleby, John A. D. ;

Mao, Xuerong ;

Wu, Huizhong .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2010, 42 (02) :646-678

[3] Existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay [J].

Bao, Haibo ;

Cao, Jinde .

APPLIED MATHEMATICS AND COMPUTATION, 2009, 215 (05) :1732-1743

[4]

Billingsley P., 1999, CONVERGE PROBAB MEAS, V2nd, DOI DOI 10.1002/9780470316962

[5] A Note on Euler Approximations for Stochastic Differential Equations with Delay [J].

Gyoengy, Istvan ;

Sabanis, Sotirios .

APPLIED MATHEMATICS AND OPTIMIZATION, 2013, 68 (03) :391-412

[6] Razumikhin-type theorems on stability of neutral stochastic functional differential equations [J].

Huang, Lirong ;

Deng, Feiqi .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2008, 53 (07) :1718-1723

[7]

Ikeda N., 1989, Stochastic differential equations and diffusion processes

[8] Some analytic approximations for neutral stochastic functional differential equations [J].

Jankovic, Svetlana ;

Vasilova, Maja ;

Krstic, Marija .

APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (08) :3615-3623

[9] Neutral stochastic differential delay equations with Markovian switching [J].

Kolmanovskii, V ;

Koroleva, N ;

Maizenberg, T ;

Mao, X ;

Matasov, A .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2003, 21 (04) :819-847

[10]

Kunita H, 2004, TRENDS MATH, P305

← 1 2 3 →