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C. R. Acad. Sci. Paris, Ser. I 336 (2003) 661666 Probability Theory
 

Summary: C. R. Acad. Sci. Paris, Ser. I 336 (2003) 661­666
Probability Theory
A Bismut type formula for the Hessian of heat semigroups
Une formule de Bismut pour la hessienne d'un semigroupe
de la chaleur
Marc Arnaudon a
, Holger Plank b
, Anton Thalmaier c,
a Département de mathématiques, Université de Poitiers, Téléport 2, BP 30179, 86962 Futuroscope Chasseneuil cedex, France
b Universität Regensburg, NWF I, Mathematik, 93040 Regensburg, Germany
c Université d'Evry, laboratoire d'analyse et probabilité, département de mathématiques,
bd François Mitterrand, 91025 Evry cedex, France
Received 3 March 2003; accepted 4 March 2003
Presented by Paul Malliavin
Abstract
We obtain an intrinsic version of a Bismut type formula for the Hessian of heat semigroups, resp. harmonic functions,
by computing second order directional derivatives of families of martingales, along with filtering of redundant noise. As
applications we provide a Hessian estimate in the general case as well as a slightly improved one in the radially symmetric
situation. To cite this article: M. Arnaudon et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).
2003 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. All rights reserved.

  

Source: Arnaudon, Marc - Département de mathématiques, Université de Poitiers
Thalmaier, Anton - Laboratoire de Mathématiques, Université du Luxembourg

 

Collections: Mathematics