Abstract
In this paper, we study stochastic differential equations with boundary conditions at the endpoints of a time interval (instead of the customary initial condition). We present existence and uniqueness results and study the Markov property of the solution. In the one-dimensional case, we prove that the solution is a Markov field $\operatorname{iff}$ the drift is affine.
Citation
D. Nualart. E. Pardoux. "Boundary Value Problems for Stochastic Differential Equations." Ann. Probab. 19 (3) 1118 - 1144, July, 1991. https://doi.org/10.1214/aop/1176990337
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