On existence and local stability of solutions of stochastic differential equations

被引：0

作者：

Chen, ZJ ^{[1
]}

机构：

[1] Shandong Univ, Dept Math, Jinan 250100, Peoples R China

来源：

STOCHASTIC ANALYSIS AND APPLICATIONS | 2001年 / 19卷 / 05期

基金：

中国国家自然科学基金;

关键词：

D O I：

10.1081/SAP-120000218

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the following stochastic differential equation: X = Phi (X) + F(X).M where F(X).M := integral F-0(X)(s)dM(s) and (M-t) is a semimartingale with M-0 = 0. We show the existence and local stability of the above stochastic differential equation. Our results generalize the corresponding results in [1], [2] and [3].

引用

页码：703 / 714

页数：12

共 50 条

[21] Nonlocal stochastic differential equations: Existence and uniqueness of solutions
Lorenz T.
SeMA Journal, 2010, 51 (1): : 99 - 107
[22] Existence and uniqueness of solutions of stochastic functional differential equations
von Renesse, Max-K.
Scheutzow, Michael
RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2010, 18 (03) : 267 - 284
[23] EXISTENCE AND STABILITY OF MILD SOLUTIONS TO IMPULSIVE STOCHASTIC NEUTRAL PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS
He, Danhua
Xu, Liguang
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2013,
[24] ON EXISTENCE AND STABILITY OF WEAK SOLUTIONS OF MULTIDIMENSIONAL STOCHASTIC DIFFERENTIAL-EQUATIONS WITH MEASURABLE COEFFICIENTS
ROZKOSZ, A
SLOMINSKI, L
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1991, 37 (02) : 187 - 197
[25] Existence and exponential stability of almost automorphic mild solutions for stochastic functional differential equations
Cao, Junfei
Yang, Qigui
Huang, Zaitang
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2011, 83 (03) : 259 - 275
[26] EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR STOCHASTIC IMPULSIVE DIFFERENTIAL EQUATIONS
Shen, Lijuan
Sun, Jitao
STOCHASTICS AND DYNAMICS, 2010, 10 (03) : 375 - 383
[27] EXISTENCE OF SOLUTIONS TO STOCHASTIC DIFFERENTIAL EQUATIONS WITH CURRENT VELOCITIES
Azaria, S. V.
Gliklikh, Yu. E.
BULLETIN OF THE SOUTH URAL STATE UNIVERSITY SERIES-MATHEMATICAL MODELLING PROGRAMMING & COMPUTER SOFTWARE, 2015, 8 (04): : 100 - 106
[28] Existence theorems for viable solutions of Stochastic differential equations
Levakov, AA
DIFFERENTIAL EQUATIONS, 2003, 39 (02) : 226 - 233
[29] On stability of solutions of stochastic delay differential equations
Ngoc, Pham Huu Anh
Tran, Ky Quan
SYSTEMS & CONTROL LETTERS, 2022, 169
[30] ON THE STABILITY OF SOLUTIONS TO CONFORMABLE STOCHASTIC DIFFERENTIAL EQUATIONS
Xiao, Guanli
Wang, Jinrong
MISKOLC MATHEMATICAL NOTES, 2020, 21 (01) : 509 - 523

← 1 2 3 4 5 →