We consider a sequence of additive functionals {φn}, set on a sequence of Markov chains {Xn} that weakly converges to a Markov process X. We give sufficient condition for such a sequence to converge in distribution, formulated in terms of the characteristics of the additive functionals, and related to the Dynkin’s theorem on the convergence of W -functionals. As an application of the main theorem, the general sufficient condition for convergence of additive functionals in terms of transition… Expand

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I . The development of I . I . Gikhman ’ s idea concerning the methods for investigating local behavior of diffusion processes and their weakly convergent sequences

Probab . Theory and Math . Stat .

1994

The development of I . I . Gikhman ’ s idea concerning the methods for investigating local behavior of diffusion processes and their weakly convergent sequences , Probab