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Integrability of Functionals of Dirichlet Processes, Probabilistic Representations of Semigroups, and Estimates of Heat Kernels

โœ Scribed by John Lunt; T.J Lyons; T.S Zhang

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
317 KB
Volume
153
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

This paper consists of three parts. In Part I, we obtain results on the integrability of functional (of exponential type) of Dirichlet processes. In Part II, we give a striking probabilistic representation of semigroup (probably non-Markovian) associated with a non-divergence operator. Part III is devoted to perturbation bounds on the operator norm of semigroups and a new (short) proof of the off-diagonal estimates of the heat kernel associated with a divergence operator. The theory of Dirichlet forms and forward, backward martingales decompositions play a central role in the whole paper.

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