A second-order Stratonovich differential equation with boundary conditions
In this paper we show that the solution of a second-order stochastic differential equation with diffusion coefficient and boundary conditions X0 = 0 and X1 = 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.
Volume (Year): 68 (1997)
Issue (Month): 1 (May)
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- Nualart, David & Pardoux, Etienne, 1991. "Second order stochastic differential equations with Dirichlet boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 39(1), pages 1-24, October.
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