On moment behavior of a class of stochastic difference equations

We consider a class of stochastic difference equations whose solutions are projections of vector Markov processes. It is shown that the Chapman-Kolmogorov equation leads to useful recurrence integral relations for determining the moments of the solution process; the simple moments at a given time can be generated directly and the mixed moments can be determined using the method of Kronecker products. This formulation also has the advantage that, under certain conditions, the asymptotic behavior of the moments can be predicted by means of the Jentzsch's theorem.