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.
Citation:
V. P. Maslov, A. M. Chebotarev, “Second term of the logarithmic asymptotics of path integrals”, Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern., 19, VINITI, Moscow, 1982, 127–154; J. Soviet Math., 23:5 (1983), 2580–2598
\Bibitem{MasChe82}
\by V.~P.~Maslov, A.~M.~Chebotarev
\paper Second term of the logarithmic asymptotics of path integrals
\serial Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern.
\yr 1982
\vol 19
\pages 127--154
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intv51}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=657959}
\zmath{https://zbmath.org/?q=an:0531.28014|0558.28009}
\transl
\jour J. Soviet Math.
\yr 1983
\vol 23
\issue 5
\pages 2580--2598
\crossref{https://doi.org/10.1007/BF01084705}
Linking options:
https://www.mathnet.ru/eng/intv51
https://www.mathnet.ru/eng/intv/v19/p127
This publication is cited in the following 5 articles:
V. P. Maslov, “Ultra-Second Quantization and “Ghosts” in Quantized Entropy”, Theoret. and Math. Phys., 129:3 (2001), 1694–1716
V. I. Piterbarg, V. R. Fatalov, “The Laplace method for probability measures in Banach spaces”, Russian Math. Surveys, 50:6 (1995), 1151–1239
V. P. Maslov, “Geometric “quantization” of thermodynamics and statistical corrections at critical points”, Theoret. and Math. Phys., 101:3 (1994), 1466–1472
V. I. Bogachev, O. G. Smolyanov, “Analytic properties of infinite-dimensional distributions”, Russian Math. Surveys, 45:3 (1990), 1–104
V. R. Struletskaya, V. Yu. Subochev, A. M. Chebotarev, “A series of invariant characteristics of extremum and the logarithmic asymptotic of Laplace integrals”, Math. Notes, 37:4 (1985), 303–307
Citation in format AMSBIB
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