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A second-order Stratonovich differential equation with boundary conditions

Author

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  • Alabert, Aureli
  • Nualart, David

Abstract

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.

Suggested Citation

  • Alabert, Aureli & Nualart, David, 1997. "A second-order Stratonovich differential equation with boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 68(1), pages 21-47, May.
    • Handle: RePEc:eee:spapps:v:68:y:1997:i:1:p:21-47
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    References listed on IDEAS

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    1. 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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