Moment identities for Poisson-Skorohod integrals and application to measure invariance

DOI10.1016/j.crma.2009.07.010zbMath1179.60035OpenAlexW2092595779MaRDI QIDQ841296

Nicolas Privault

Publication date: 15 September 2009

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2009.07.010

zbMATH Keywords

Malliavin calculusPoisson spaceSkorohod integralinduced measures

Mathematics Subject Classification ID

Stochastic calculus of variations and the Malliavin calculus (60H07) Continuity and singularity of induced measures (60G30)

Related Items (11)

Moments of Markovian growth–collapse processes ⋮ Invariance of Poisson measures under random transformations ⋮ Factorial moments of point processes ⋮ Combinatorics of Poisson Stochastic Integrals with Random Integrands ⋮ Heavy-traffic approximations for fractionally integrated random walks in the domain of attraction of a non-Gaussian stable distribution ⋮ Girsanov identities for Poisson measures under quasi-nilpotent transformations ⋮ Nonstationary shot noise modeling of neuron membrane potentials by closed-form moments and Gram-Charlier expansions ⋮ Laplace transform identities and measure-preserving transformations on the Lie-Wiener-Poisson spaces ⋮ Moments of k-hop counts in the random-connection model ⋮ Mixing of Poisson random measures under interacting transformations ⋮ Cardinality estimation for random stopping sets based on Poisson point processes

Cites Work

• Stochastic analysis in discrete and continuous settings. With normal martingales.
• Moment identities for Skorohod integrals on the Wiener space and applications
• Random rotations of the Wiener path
• Duality formulas on the Poisson space
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