Abstract
The paper deals with an integral functional on a stationary random mixing field and on a solution of the stochastic equation which depend on a small parameter. The type of the functional is conditioned by the probabilistic representation of solutions of the Cauchy problem and the first boundaryvalue problem for a linear second-order parabolic equation in a nondivergent form with unbounded quick random oscillations of the zero-order term of the derivative. The central limit theorem of convergence of the functional is proved.
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Translated from Ukrains’kiíĭ Matematychnyĭ Visnyk, Vol. 12, No. 3, pp. 335–362, July–August, 2015.
The work was executed under the support of a grant of the NASU–RFFS No. 09-01-14.
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Granovski, Y.I., Makhno, S.Y. Homogenization of random functionals on solutions of stochastic equations. J Math Sci 214, 186–199 (2016). https://doi.org/10.1007/s10958-016-2768-3
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DOI: https://doi.org/10.1007/s10958-016-2768-3