Nualart, DavidPardoux, E.2015-03-112015-03-111991Nualart, D.; Pardoux, E. Boundary Value Problems for Stochastic Differential Equations. Ann. Probab. 19 (1991), no. 3, 1118--1144. http://dx.doi.org/10.1214/aop/1176990337.https://hdl.handle.net/1808/17060This is the published version, also available here: http://dx.doi.org/10.1214/aop/1176990337.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 iff the drift is affine.Stochastic differential equationsequations with boundary conditionsMarkov processesMarkov fieldsArticle10.1214/aop/1176990337openAccess