In this paper we show that the solution of a second-order stochastic differential equation with diffusion coefficient and boundary conditions X0 = 0 and X1 = 1 is a 2-Markov field if and only if the drift is a linear function. The proof is based on the method of change of probability and makes...

We consider one-dimensional differential equations with a boundary condition on the interval [0,1], perturbed by a Poisson noise. We study existence and uniqueness, the law of the solution and in which cases the solution is a reciprocal process.