Abstract
In the survey results are presented related to the construction of asymptotic expansions of Green's function of the Cauchy problem for the heat equation. The basic attention is devoted to the first two terms of the logarithmic asymptotics which are obtained “locally” by probabilistic methods and “globally” by the method of convolution of the sequence of asymptotic solutions over small time.
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Translated from Itogi Nauki i Tekhniki, Seriya Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 19, pp. 127–154, 1982.
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Maslov, V.P., Chebotarev, A.M. Second term of the logarithmic asymptotics of path integrals. J Math Sci 23, 2580–2598 (1983). https://doi.org/10.1007/BF01084705
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DOI: https://doi.org/10.1007/BF01084705