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.
Publié le : 1991-07-14
Classification:
Stochastic differential equations,
equations with boundary conditions,
Markov processes,
Markov fields,
34K10,
60H10
@article{1176990337,
author = {Nualart, D. and Pardoux, E.},
title = {Boundary Value Problems for Stochastic Differential Equations},
journal = {Ann. Probab.},
volume = {19},
number = {4},
year = {1991},
pages = { 1118-1144},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990337}
}
Nualart, D.; Pardoux, E. Boundary Value Problems for Stochastic Differential Equations. Ann. Probab., Tome 19 (1991) no. 4, pp. 1118-1144. http://gdmltest.u-ga.fr/item/1176990337/