An example of non-Markovian stochastic two-point boundary value problem.

In this paper we first present a multidimensional version of the characterization of the conditional independence in terms of a factorization property proved by Alabert et al. in the scalar case. As an application, we prove that the solution of a particular two-dimensional linear stochastic differential equation with boundary condition, considered by Ocone and Pardoux, is not a Markov field