2ND-ORDER STOCHASTIC DIFFERENTIAL-EQUATIONS WITH DIRICHLET BOUNDARY-CONDITIONS
[摘要] We consider the second order stochastic differential equation X(t) + f(X(t), X(t)) = W(t) where t runs on the interval [0, 1], {W(t)} is an ordinary Brownian motion and we impose the Dirichlet boundary conditions X(0) = a and X(1) = b. We show pathwise existence and uniqueness of a solution assuming some smoothness and monotonicity conditions on f, and we study the Markov property of the solution using an extended version of the Girsanov theorem due to Kusuoka.
[发布日期] 1991-10-01 [发布机构]
[效力级别] [学科分类]
[关键词] STOCHASTIC DIFFERENTIAL EQUATIONS;MARKOV PROCESSES;NONCAUSAL STOCHASTIC CALCULUS;SKOROHOD AND STRATONOVICH STOCHASTIC INTEGRALS;ANTICIPATING GIRSANOV TRANSFORMATION [时效性]
