文献类型：期刊文献

英文题名：Existence conditions and variational approach for adapted solutions of the two-point boundary value problem of stochastic differential equations

作者：Xia, Ning-Mao[1];Lin, Ai-Hong[1]

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2011

卷号：217

期号：20

起止页码：7900

外文期刊名：APPLIED MATHEMATICS AND COMPUTATION

收录：;EI(收录号：20112113997875);WOS:【SCI-EXPANDED(收录号:WOS:000290570000005)】；

语种：英文

外文关键词：Two-point boundary value problem; Stochastic differential equation; Variational approach; Continuous dependence

摘要：This paper considers the two-point boundary value problem of stochastic differential equation with the following form: dX(t) = f(t, X(t))dt + sigma(t, X(t))dW(t), AX(0) + BX(T) = xi*, The sufficient and necessary conditions are given for the existence of the adapted solutions. In the simple case that f(t, X(t)) = f(t), the solution can be obtained by introducing a control term ft, extending the solution from X(t) to (X(t), f(t)), and constructing a process sequence. All the results obtained are compared with those related to the eigenvalue problems, and the "martingale approach'' solution proposed by Pardoux and Peng for backward stochastic differential equations. (C) 2011 Elsevier Inc. All rights reserved.