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.
Mots clés : stochastic Taylor expansions, index theorems
@article{PS_2012__16__453_0, author = {Baudoin, Fabrice}, title = {Stochastic {Taylor} expansions and heat kernel asymptotics}, journal = {ESAIM: Probability and Statistics}, pages = {453--478}, publisher = {EDP-Sciences}, volume = {16}, year = {2012}, doi = {10.1051/ps/2011107}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps/2011107/} }
TY - JOUR AU - Baudoin, Fabrice TI - Stochastic Taylor expansions and heat kernel asymptotics JO - ESAIM: Probability and Statistics PY - 2012 SP - 453 EP - 478 VL - 16 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2011107/ DO - 10.1051/ps/2011107 LA - en ID - PS_2012__16__453_0 ER -
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://www.numdam.org/articles/10.1051/ps/2011107/
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