Weak convergence of Markov processes with extended generators
The author extends the concept of generator of a Markov process and obtains sufficient conditions of the weak convergence of Markov processes (solutions of local martingale problems) in terms of the convergence of their extended generators. The result includes the case of continuous time Markov chains. For Markov processes with generators in Dynkin sense, necessary and sufficient conditions are investigated. As an application, some sufficient conditions for the weak convergence of diffusion processes with jumps are also given.
scientific article; zbMATH DE number 828381