Functional limit theorems for nonhomogeneous Markov chains. (Russian) Zbl 0669.60036

Anisimov, V. V.

Teor. Veroyatn. Mat. Stat., Kiev 39, 5-11 (1988).

The weak convergence in D[0,1] of random processes generated by the sequence of the partial sums of measurable functions on a general Markov chain (the invariance principle) is studied. Under some restrictions on the second moments of the processes and the ergodicity coefficient of the chain it is proved that the weak limit of such processes will be Gaussian with independent increments.

Reviewer: I.S.Borisov

MSC:

60F17	Functional limit theorems; invariance principles
60J10	Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords:

invariance principle; Markov chain; ergodicity coefficient