A second-order Stratonovich differential equation with boundary conditions

In this paper we show that the solution of a second-order stochastic differential equation with diffusion coefficient σXdot1 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 use of the techniques of Malliavin calculus.