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Ben Arous, G.; Léandre, R.

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

Probab. Theory Relat. Fields 90, No. 2, 175-202 (1991).
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

Cited in 1 Review
Cited in 21 Documents

MSC:

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

Keywords:

large deviations theory; heat kernel of a degenerate diffusion; exponential decay over the diagonal; Malliavin calculus

Citations:

Zbl 0734.60027
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\textit{G. Ben Arous} and \textit{R. Léandre}, Probab. Theory Relat. Fields 90, No. 2, 175--202 (1991; Zbl 0734.60026)
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References:

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