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

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
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