### LIMIT THEOREMS FOR OSCILLATORY FUNCTIONALS OF A MARKOV PROCESS

**TARAS O. ANDROSHCHUK AND ALEXEY M. KULIK**

*Theory of Stochastic Processes Vol. 11 (27), no. 3–4, 2005, pp. 3–13*

We study the limit behavior of a family of functionals from a given Markov process which are called oscillatory functionals. The typical oscillatory functional is homogeneneous and non-negative but neither additive nor continuous. We claim that the discontinuity and non-additivity of functionals from a given family vanish in the limit and, in this framework, prove a generalization of the theorem by E.B. Dynkin on the convergence of a family of

*W*-functionals.

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