Abstract:
Let xεs be a diffusion process with the infinitesimal operator given by (3), and let pε(t,x,y) be the transition probability density of xεs. The aim of the article is to prove that the asymptotics of pε(t,x,y) has the form of (4) if t and the distance between x and y are sufficiently small. We calculate the principal term of the asymptotics and deduce recurrent formulas for the others.
Citation:
Yu. I. Kifer, “On the asymptotics of the transition probability density of processes with small diffusion”, Teor. Veroyatnost. i Primenen., 21:3 (1976), 527–536; Theory Probab. Appl., 21:3 (1977), 513–522
\Bibitem{Kif76}
\by Yu.~I.~Kifer
\paper On the asymptotics of the transition probability density of processes with small diffusion
\jour Teor. Veroyatnost. i Primenen.
\yr 1976
\vol 21
\issue 3
\pages 527--536
\mathnet{http://mi.mathnet.ru/tvp3397}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=431398}
\zmath{https://zbmath.org/?q=an:0367.60035}
\transl
\jour Theory Probab. Appl.
\yr 1977
\vol 21
\issue 3
\pages 513--522
\crossref{https://doi.org/10.1137/1121063}
Linking options:
https://www.mathnet.ru/eng/tvp3397
https://www.mathnet.ru/eng/tvp/v21/i3/p527
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H. R. Jauslin, “A classification of Fokker-Planck models and the small and large noise asymptotics”, J Stat Phys, 40:1-2 (1985), 147
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