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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