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Prob. Theory and Math. Stat., pp. 2332 B. Grigelionis et al. (Eds)
 

Summary: Prob. Theory and Math. Stat., pp. 23­32
B. Grigelionis et al. (Eds)
© 1999 VSP/TEV
BISMUT TYPE DIFFERENTIATION OF SEMIGROUPS
MARC ARNAUDON
Institut de Recherche Mathématique Avancée, Université Louis Pasteur,
7, rue René Descartes, F­ 67084 Strasbourg Cedex, France
ANTON THALMAIER
Institut für Angewandte Mathematik, Universität Bonn, Wegelerstraße 6,
D ­ 53115 Bonn, Germany
ABSTRACT
We present a unified approach to Bismut type differentiation formulas for heat semigroups on functions
and forms. Both elliptic and hypoelliptic situations are considered. Nonlinear extensions apply to the
case of harmonic maps between Riemannian manifolds and solutions to the nonlinear heat equation.
1. INTRODUCTION
Let M be a smooth n-dimensional manifold. On M consider a Stratonovich SDE
with smooth coefficients of the type
X = A(X) Z + A0(X) dt, (1.1)
where A0 (T M) is a vector field and A: M × Rr T M, (x, z) A(x)z a
bundle map over M for some r. The driving process Z is assumed to be an Rr-valued

  

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

 

Collections: Mathematics