Articlegreen1991

Boundary Value Problems for Stochastic Differential Equations

58 citations0/0 files storedThe Annals of Probability

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Differential Equations and Boundary Problems

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.

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