Equivalence of Gradients on Configuration Spaces (1999)
| Venue: | Random Operators and Stochastic Equations |
| Citations: | 10 - 4 self |
BibTeX
@ARTICLE{Privault99equivalenceof,
author = {Nicolas Privault},
title = {Equivalence of Gradients on Configuration Spaces},
journal = {Random Operators and Stochastic Equations},
year = {1999},
volume = {7}
}
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Abstract
The gradient on a Riemannian manifold X is lifted to the configuration space \Upsilon X on X via a pointwise identity. This entails a norm equivalence that either holds under any probability measure or characterizes the Poisson measures, depending on the tangent space chosen on \Upsilon X . More generally, this approach links carr'e du champ operators on X to their counterparts on \Upsilon X , and also includes structures that do not admit a gradient. Key words: Configuration spaces, Poisson measures, Stochastic analysis. Mathematics Subject Classification (1991): 58G32, 60H07, 60J45, 60J75. 1 Introduction Stochastic analysis under Poisson measures, cf. [5], [6], has been developed in several different directions. This is mainly due to the fact that, unlike on the Wiener space, the gradient on Fock space and the infinitesimal Poisson gradient do not coincide under the identification of the Fock space to the L 2 space of the Poisson process. - The gradient on Fock space is in...
