Wick calculus on spaces of generalized functions of compound Poisson white noise

DOI10.1016/S0034-4877(97)88002-0zbMath0892.60051MaRDI QIDQ1373676

G. V. Shchepan'uk, Eugene W. Lytvynov, Alexei L. Rebenko

Publication date: 17 December 1997

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Fock spaceAppell polynomialsWick calculuscompound Poisson white noiseGaussian white noise calculusnon-Gaussian biorthogonal analysis

Mathematics Subject Classification ID

Generalized stochastic processes (60G20) Markov processes (60J99) Distributions on infinite-dimensional spaces (46F25)

Related Items (12)

OPERATORS OF GAMMA WHITE NOISE CALCULUS ⋮ HARMONIC ANALYSIS ON CONFIGURATION SPACE I: GENERAL THEORY ⋮ Quantum mathematics: backgrounds and some applications to nonlinear dynamical systems ⋮ The Segal-Bargmann transform for Lévy functionals ⋮ Estimation of robot states with Poisson process based on EKF approximate of Kushner filter: a completely coordinate free Lie group approach ⋮ The Segal-Bargmann transform for Lévy white noise functionals associated with non-integrable Lévy processes ⋮ ORTHOGONAL DECOMPOSITIONS FOR LÉVY PROCESSES WITH AN APPLICATION TO THE GAMMA, PASCAL, AND MEIXNER PROCESSES ⋮ Introductive backgrounds to modern quantum mathematics with application to nonlinear dynamical systems ⋮ Pascal white noise calculus ⋮ Analysis of generalized Lévy white noise functionals ⋮ Analysis on Poisson and Gamma Spaces ⋮ Lévy white noise calculus based on interaction exponents

Cites Work

• Quantum Ito's formula and stochastic evolutions
• Distributions sur l'espace de P. Lévy et calcul stochastique. (Distributions on P. Lévy's space and stochastic calculus)
• Quantum probability for probabilists
• Integration by parts for Poisson processes
• A note on spaces of test and generalized functions of Poisson white noise
• White noise calculus and Fock space
• Spaces of white noise distributions: Constructions, descriptions, applications. I
• Wick theorems in non-Gaussian white noise calculus
• Generalized Poisson functionals
• Non-Gaussian infinite dimensional analysis
• Spectral Type of the Shift Transformation of Differential Processes With Stationary Increments
• Calculus on Gaussian and Poisson white noises
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• On the Poisson integrals representation in the classical statistical mechanics of continuous systems
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