A second-order Stratonovich differential equation with boundary conditions

[摘要] In this paper we show that the solution of a second-order stochastic differential equation with diffusion coefficient sigma(X) over dot(t) and boundary conditions X-0 = 0 and X-1 = 1 is a 2-Markov field if and only if the drift is a linear function. The proof is based on the method of change of probability and makes use of the techniques of Malliavin calculus.

[发布日期] 1997-05-30

[关键词] stochastic differential equations;Markov fields;non-causal stochastic calculus;Girsanov transformations