A note on the carr\'e du champ on the Poisson space
Ronan Herry
TL;DR
This paper provides a general representation of the carré du champ operator for the Ornstein-Uhlenbeck semi-group on the Poisson space, expressed through add-one and drop-one operators.
Contribution
It establishes, in complete generality, the representation of the carrée du champ operator on the Poisson space using add-one and drop-one operators.
Findings
Representation of the carrée du champ operator in terms of add-one and drop-one operators.
Generalization to complete settings for the Poisson space.
Theoretical framework for analysis on Poisson spaces.
Abstract
The goal of this short note is to establish, in complete generality, the representation for the carr\'e du champ operator associated with the Ornstein-Uhlenbeck semi-group on the Poisson space in terms of the add-one and drop-one operators.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Operator Algebra Research · Advanced Topics in Algebra