Fixed point technique for a class of backward stochastic differential equations

被引：1

作者：

Negrea, Romeo ^{[1
]}

Preda, Ciprian ^{[2
]}

机构：

[1] Politech Univ Timisoara, Dept Math, Timisoara 300006, Romania

[2] West Univ Timisoara, Fac Econ & Business Adm, Timisoara 300223, Romania

来源：

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS | 2013年 / 6卷 / 01期

关键词：

Backward stochastic differential equations; non-Lipschitz conditions; adapted solutions; pathwise uniqueness; global solutions; fixed point technique; Schauder's fixed point theorem; EXISTENCE; UNIQUENESS;

D O I：

10.22436/jnsa.006.01.07

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish a new theorem on the existence and uniqueness of the adapted solution to backward stochastic differential equations under some weaker conditions than the Lipschitz one. The extension is based on Athanassov's condition for ordinary differential equations. In order to prove the existence of the solutions we use a fixed point technique based on Schauder's fixed point theorem. Also, we study some regularity properties of the solution for this class of stochastic differential equations.

引用

页码：41 / 50

页数：10

共 27 条

[21]

NEGREA R, 2003, ANALELE U BUCUREST M, V52, P225

[22]

Negrea R., 2011, DYN CONTIN DISCRET I, V18, P485

[23]

Negrea R., EXISTENCE U IN PRESS

[24]

Negrea R, 2008, FIXED POINT THEORY, V9, P199

[25] Backward stochastic differential equations with subdifferential operator and related variational inequalities [J].

Pardoux, E ;

Rascanu, A .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1998, 76 (02) :191-215

[26] ADAPTED SOLUTION OF A BACKWARD STOCHASTIC DIFFERENTIAL-EQUATION [J].

PARDOUX, E ;

PENG, SG .

SYSTEMS & CONTROL LETTERS, 1990, 14 (01) :55-61

[27] BACKWARD STOCHASTIC DIFFERENTIAL-EQUATIONS AND APPLICATIONS TO OPTIMAL-CONTROL [J].

PENG, SG .

APPLIED MATHEMATICS AND OPTIMIZATION, 1993, 27 (02) :125-144

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