SECOND ORDER APPROXIMATION TO STOCHASTIC DIFFERENTIAL EQUATIONS FOR BACKWARD PROCESSES AND GAUSSIAN DISTRIBUTIONS

摘要

An iterative procedure to solve the restoration problem is proposed. The solution reduces to a simple filtration problem. This technique can be used to derive stochastic differential equations which are satisfied by trajectories of Markov diffusion processes in reverse time observation. It was found that drift coefficients are expressed only in terms of its unconditional distribution density, while the diffusion coefficients do not change. The particular case of non-linear stochastic systems with potential function is also considered. Using our technique, the problem reduces to a simple differential equation.