Literature cited
V. V. Zhikov, S. M. Kozlov, and O. A. Oleinik, “On the G-convergence of parabolic operators,” Usp. Mat. Nauk,36, No. 1 (217), 11–58 (1981).
R. Z. Khas'minskii, “On the averaging principle for parabolic and elliptic differential equations and Markov processes with small diffusion,” Teor. Veroyatn. Primen.,8, No. 1, 3–25 (1963).
A. D. Venttsel' and M. I. Freidlin, Fluctuations in Dynamical Systems Subject to Small Random Perturbations [in Russian], Nauka, Moscow (1979).
A. D. Borisenko, “On the asymptotic behavior of the solution of the Cauchy problem for a parabolic equation,” Teor. Veroyatn. Mat. Statist., No. 17, 23–28 (1977).
A. D. Borisenko, “The asymptotic behavior of the solution of the Cauchy problem for an equation of parabolic type,” Teor. Veroyatn. Mat. Statist., No. 20, 25–30 (1979).
I. I. Gikhman (Gihman) and A. V. Shorokhod (Skorohod), The Theory of Stochastic Processes. III, Springer, New York (1979).
G. L. Kulinich, “On the limiting behavior of the solutions of stochastic differential equations of diffusion type with random coefficients,” in: Limit Theorems for Random Processes [in Russian], Inst. Mat., Akad. Nauk Ukr. SSR, Kiev (1977), pp. 137–151.
A. Friedman, Stochastic Differential Equations and Applications, Vol. 1, Academic Press, New York (1975).
E. B. Dynkin, “Functionals of rajectories of Markov random processes,” Dokl. Akad. Nauk SSSR,104, No. 5, 691–694 (1955).
A. V. Skorokhod, Studies in the Theory of Random Processes, Addison-Wesley, Reading (1965).
I. I. Gikhman (Gihman) and A. V. Shorokhod (Skorohod), The Theory of Stochastic Processes. I, Springer, New York (1974).
N. V. Krylov, Controlled Diffusion Processes, Springer, New York (1980).
A. D. Borisenko, “The distribution of an additive functional of a diffusion process,” Teor. Veroyatn. Mat. Statist., No. 28, 5–9 (1983).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 6, pp. 732–738, June, 1989.
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Borisenko, A.D. Limiting behavior of the solution of the Cauchy problem for a parabolic equation. Ukr Math J 41, 629–634 (1989). https://doi.org/10.1007/BF01060558
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DOI: https://doi.org/10.1007/BF01060558