Solving approximately a prediction problem for stochastic jump-diffusion systems

In this paper, a new approach to solving a prediction problem for nonlinear stochastic differential systems with a Poisson component is discussed. In this approach, the prediction problem is reduced to an analysis of stochastic jump-diffusion systems with terminating and branching paths. The prediction problem can be approximately solved by using numerical methods for stochastic differential equations and methods for modeling inhomogeneous Poisson flows.