Limit Theorems for Markov Processes

General theorems obtained in [1] are used to obtain concrete results for Markov processes. These results are formulated in terms of infinitesimal operators of Markov processes (see [13]). It is proved, with some general assumptions made, that the convergence of initial distributions and infinitesimal operators of processes is entailed with the convergence of distributions of $\mathrm J_1$-continuous functionals of these processes (see [1]).