Stochastic Taylor expansions and heat kernel asymptotics
ESAIM: Probability and Statistics, Tome 16 (2012), pp. 453-478.

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.

DOI : 10.1051/ps/2011107
Classification : 60H30, 58J20
Mots clés : stochastic Taylor expansions, index theorems 
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Baudoin, Fabrice. Stochastic Taylor expansions and heat kernel asymptotics. ESAIM: Probability and Statistics, Tome 16 (2012), pp. 453-478. doi : 10.1051/ps/2011107. http://archive.numdam.org/articles/10.1051/ps/2011107/

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