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- Title
SHORT TIME FULL ASYMPTOTIC EXPANSION OF HYPOELLIPTIC HEAT KERNEL AT THE CUT LOCUS.
- Authors
YUZURU INAHAMA; SETSUO TANIGUCHI
- Abstract
In this paper we prove a short time asymptotic expansion of a hypoelliptic heat kernel on a Euclidean space and a compact manifold. We study the 'cut locus' case, namely, the case where energyminimizing paths which join the two points under consideration form not a finite set, but a compact manifold. Under mild assumptions we obtain an asymptotic expansion of the heat kernel up to any order. Our approach is probabilistic and the heat kernel is regarded as the density of the law of a hypoelliptic diffusion process, which is realized as a unique solution of the corresponding stochastic differential equation. Our main tools are S. Watanabe's distributional Malliavin calculus and T. Lyons' rough path theory.
- Subjects
ASYMPTOTIC expansions; HYPOELLIPTIC differential equations; MALLIAVIN calculus; EUCLIDEAN domains; STOCHASTIC difference equations
- Publication
Forum of Mathematics, Sigma, 2017, Vol 5, p1
- ISSN
2050-5094
- Publication type
Article
- DOI
10.1017/fms.2017.14