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Stochastic Taylor expansions and heat kernel asymptotics∗

Published online by Cambridge University Press:  31 October 2012

Fabrice Baudoin
Fabrice Baudoin*
Affiliation:
Department of Mathematics Purdue University, 504 Northwestern, Avenu West Lafayette, Indiana, USA. [email protected]
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Abstract

These notes focus on the applications of the stochastic Taylor expansion of solutions of stochastic differential equations to the study of heat kernels in small times. As an illustration of these methods we provide a new heat kernel proof of the Chern–Gauss–Bonnet theorem.

Keywords

Stochastic Taylor expansionsIndex theorems
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 16 , 2012 , pp. 453 - 478
Copyright
© EDP Sciences, SMAI, 2012

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References

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