Averaging for partial differential equations whose coefficients are perturbed by jump Markov processes - Kolomiets , Yu. V. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
Weak convergence in the sense of distributions of the solutions of parabolic–type partial differential equations with periodic rapidly oscillating coefficients perturbed by jump–like Markov processes that function in “rapid” time with finite state set is considered. The weak compactness of the measures generated by the solutions of the equations is proved and the weak convergence to a unique solution of the Martingale problem that satisfies a stochastic partial differential equation is demonstrated.