The Annals of Probability

Boundary Value Problems for Stochastic Differential Equations

D. Nualart and E. Pardoux

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 34K10: Boundary value problems
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
Stochastic differential equations equations with boundary conditions Markov processes Markov fields

Citation

Nualart, D.; Pardoux, E. Boundary Value Problems for Stochastic Differential Equations. Ann. Probab. 19 (1991), no. 3, 1118--1144. doi:10.1214/aop/1176990337. https://projecteuclid.org/euclid.aop/1176990337


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