Title :
Sobolev-Poincare type inequalities for Poisson functionals
Author :
Purtukhia, O. ; Jaoshvili, V.
Author_Institution :
A. Razmadze Math. Inst., Ivane Javakhishvili Tbilisi State Univ., Tbilisi, Georgia
Abstract :
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.
Keywords :
Hilbert spaces; stochastic processes; Poisson functionals; Sobolev type Hilbert spaces; Sobolev-Poincare type inequalities; logarithmic Sobolev type inequalities; normal martingale; random variables; stochastic derivative; Clark-Haus-smann-Ocone representations; Sobolev-Poincare type inequalities; compensated Poisson process; stochastic derivative;
Conference_Titel :
Problems of Cybernetics and Informatics (PCI), 2012 IV International Conference
Conference_Location :
Baku
Print_ISBN :
978-1-4673-4500-2
DOI :
10.1109/ICPCI.2012.6486411
