## The Annals of Probability

### Boundary Value Problems for Stochastic Differential Equations

#### 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.

#### Article information

Source
Ann. Probab., Volume 19, Number 3 (1991), 1118-1144.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176990337

Digital Object Identifier
doi:10.1214/aop/1176990337

Mathematical Reviews number (MathSciNet)
MR1112409

Zentralblatt MATH identifier
0736.60052

JSTOR