A second-order Stratonovich differential equation with boundary conditions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:68

Article

Alabert, A ; Nualart, D

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

DOI  :  10.1016/S0304-4149(97)00021-5

来源: Elsevier

【 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.

【 授权许可】

Free