SEMINAR @ SISSSA, Leandre dd 17/05/06

[Barbara Corzani]

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FUNCTIONAL ANALYSIS SECTOR'S ACTIVITIES
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SEMINAR 

Prof.
Remi Leandre,
(Univ. de Bourgogne, France)

Title:
"Malliavin Calculus of Bismut type without probability and its applications"

Wed.  17  May  2006  @  02.30 p.m.

SISSA - Main Building - ground floor - room B

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Abstract: This talk is divided in 3 parts:

-)In the first part we translate Malliavin's Calculus in order to get regularity
of heat semi-groups in semi-group theory. Probabilistic language is eliminated.

-)In the second part, we translate in semi-group theory the lower bound for
short time asymptotics of Varadhan's type for hypoelliptic heat-kernels, where
the Subriemannian metric associated to the operator plays a big role. These
estimates we got by ourself by using the Malliavin Calculus a long time ago.

-)In the third part, we translate in semi-group theory the Wong-Zakai
approximation of a diffusion. This allows us to evacuate the use of stochastic
differential equations in the proof of the theorem of Ben Arous and giving a
sufficient condition in order a heat-kernel is strictly positive, where
Bismut's condition plays a big role.