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Décroissance exponentielle du noyau de la chaleur sur la diagonale. I. (Exponential decay of the heat kernel over the diagonal. I). (French) Zbl 0734.60026
We give examples based upon large deviations theory where the heat kernel of a degenerate diffusion has an exponential decay over the diagonal. Using Malliavin calculus, we give conditions for a more generalized heat kernel to have an exponential decay over the diagonal. We give lower bound in some particular case by using the Bismut’s condition.
[For part II see the following review, Zbl 0734.60027.]
Reviewer: G.Ben Arous

MSC:
60F10 Large deviations
60J60 Diffusion processes
60H07 Stochastic calculus of variations and the Malliavin calculus
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