Sobolev-Poincare type inequalities for Poisson functionals

The Sobolev type Hilbert spaces for normal martingale is defined and stochastic derivative of Poisson functionals are introduced. The Sobolev-Poincare and logarithmic Sobolev type inequalities are proved for random variables from this spaces.

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Bibliographic Details
Main Authors: Purtukhia, O., Jaoshvili, V.
Format: Conference Proceeding
Language:English
Subjects:
Clark-Haus-smann-Ocone representations
compensated Poisson process
Sobolev-Poincare type inequalities
stochastic derivative
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Description
Summary:The Sobolev type Hilbert spaces for normal martingale is defined and stochastic derivative of Poisson functionals are introduced. The Sobolev-Poincare and logarithmic Sobolev type inequalities are proved for random variables from this spaces.
DOI:10.1109/ICPCI.2012.6486411