Abstract
Three main schemes of limit theorems for random evolutions are discussed: averaging, diffusion approximation, and the asymptotics of large deviations. Markov stochastic evolutions with locally independent increments on increasing time intervals T ε = t/ε → ∞, ε → 0, are considered. The asymptotic behavior of random evolutions is investigated with the use of solutions of the singular perturbation problems for reducibly invertible operators.
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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 8, No. 2, pp. 220–240, April–May, 2011.
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Korolyuk, V.S. Random evolutions with locally independent increments on increasing time intervals. J Math Sci 179, 273–289 (2011). https://doi.org/10.1007/s10958-011-0594-1
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DOI: https://doi.org/10.1007/s10958-011-0594-1