Abstract
We study a class of local gradient operators on Poisson space that have the derivation property. This allows us to give another example of a gra- dient operator that satisfies the hypotheses of Chapter 3, this time for a discontinuous process. In particular we obtain an anticipative extension of the compensated Poisson stochastic integral and other expressions for the Clark predictable representation formula. The fact that the gradient oper- ator satisfies the chain rule of derivation has important consequences for deviation inequalities, computation of chaos expansions, characterizations of Poisson measures, and sensitivity analysis. It also leads to the definition of an infinite dimensional geometry under Poisson measures.
Keywords
- Compact Interval
- Duality Relation
- Local Gradient
- Logarithmic Sobolev Inequality
- Wiener Space
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Privault, N. (2009). Local Gradients on the Poisson Space. In: Stochastic Analysis in Discrete and Continuous Settings. Lecture Notes in Mathematics(), vol 1982. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02380-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-02380-4_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02379-8
Online ISBN: 978-3-642-02380-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)
