Markov Field Property of Stochastic Differential Equations

This is the published version, also available here: http://dx.doi.org/10.1214/aop/1176988183.The purpose of this paper is to prove a characterization of the conditional independence of two independent random variables given a particular functional of them, in terms of a factorization property. As an application we discuss the Markov field property for solutions of stochastic differential equations with a boundary condition involving the values of the process at times t=0 and t=1