Diffusion approximation of integral functionals in merging and averaging scheme. (English. Ukrainian original) Zbl 0958.60038

Korolyuk, V. S.; Limnios, N.

Theory Probab. Math. Stat. 59, 101-107 (1999); translation from Teor. Jmorvirn. Mat. Stat. 59, 99-105 (1998).

The authors consider an integral functional \(\zeta^{\varepsilon}(t)\) with rapid Markov switchings \(x^{\varepsilon}(t)\) in series scheme of the following form: \(\zeta^{\varepsilon}(t)=\int_{0}^{t}a(x^{\varepsilon}(s)) ds\). Diffusion approximations of such integral functional in averaging and merging schemes are proposed. The diffusion approximation is constructed for the normalized and centered integral functionals.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60G25	Prediction theory (aspects of stochastic processes)
60J75	Jump processes (MSC2010)
60F17	Functional limit theorems; invariance principles
60J25	Continuous-time Markov processes on general state spaces

Keywords:

diffusion approximation; integral functionals; merging and averaging scheme