Volume 16, 2012
Special Issue: Spring School Mons Random differential equations and Gaussian fields
|Page(s)||453 - 478|
|Published online||31 October 2012|
Stochastic Taylor expansions and heat kernel asymptotics∗
Department of Mathematics Purdue University, 504 Northwestern, Avenu West Lafayette, Indiana, USA
Received: 15 July 2009
Revised: 27 April 2010
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.
Mathematics Subject Classification: 60H30 / 58J20
Key words: Stochastic Taylor expansions / Index theorems
© EDP Sciences, SMAI, 2012
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