Approximation of asymptotically consolidatable Markov processes. (English. Russian original) Zbl 0631.60064

Anisimov, V. V.

Theory Probab. Math. Stat. 34, 1-11 (1987); translation from Teor. Veroyatn. Mat. Stat. 34, 3-12 (1986).

If in \((X,R^ s)\) one considers a nonhomogeneous Markov process \((X_ n(k),\xi_ n(k))\), \(k\geq 0\), where \(\xi_ n(k)\) is a sum of conditionally independent variables on \(X_ n(k)\) and considers a measurable mapping K:X\(\to Y\), where (X,\({\mathcal B}_ X)\) and (Y,\({\mathcal B}_ Y)\) are two measurable metric spaces, the author proves the closeness of the measures generated by \((K(x_ n(k))\), \(\xi_ n(k))\) and the Markov process \((y_ n(k),\xi_ n(k))\) with characteristics averaged relating to a quasi-ergodic measure.
The author also proves, that a limit theorem for convergence to a Markov process in \((Y,R^ S)\) which is homogeneous relating to the second component, is true.

Reviewer: G.G.Vrânceanu

MSC:

60J05	Discrete-time Markov processes on general state spaces
60J25	Continuous-time Markov processes on general state spaces

Keywords:

quasi-ergodic measure; convergence to a Markov process