Abstract
The mathematical expectations of certain functionals of the solutions of stochastic equations with a time lag are discussed, and the principal terms of their asymptotic expansions as the lag tends to zero are evaluated.
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A. B. Vasil'eva and V. F. Butuzov, Asymptotic Expansions of the Solutions of Singularly Disturbed Equations [in Russian], Nauka, Moscow (1973).
L. É. Él'sgol'ts and S. B. Norkin, Introduction to the Theory of Differential Equations with a Deviating Argument [in Russian], Nauka, Moscow (1971).
E. F. Beckenbach and R. Bellman, Inequalities, Springer, Berlin (1965).
I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes [in Russian], Nauka, Moscow (1965).
A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, New York (1964).
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Translated from Matematicheskie Zametki, Vol. 17, No. 5, pp. 717–726, May, 1975.
The author thanks M. I. Freidlin for guidance.
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Kuznetsova, T.A. On stochastic differential equations with a small time lag. Mathematical Notes of the Academy of Sciences of the USSR 17, 426–432 (1975). https://doi.org/10.1007/BF01155797
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DOI: https://doi.org/10.1007/BF01155797