Probability Theory and Related Fields

, Volume 90, Issue 2, pp 175-202

First online:

Decroissance exponentielle du noyau de la chaleur sur la diagonale (I)

  • G. Ben ArousAffiliated withDepartment de Mathématiques, École Normale Supérieure
  • , R. LéandreAffiliated withUniversité Louis Pasteur

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We give examples based upon large deviation's 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.