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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.

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