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Y. Kondratiev, L. Streit, Werner Westerkamp, Jia-An Yan (1998)
Generalized functions in infinite dimensional analysisHiroshima Mathematical Journal, 28
Z. Huang, Ying Wu (2004)
Interacting Fock Expansion of Lévy White Noise FunctionalsActa Applicandae Mathematica, 82
B. Simon (1974)
The P(φ)[2] Euclidean (quantum) field theory
Y. Kondratiev, E. Lytvynov (2000)
Operators of Gamma White Noise CalculusInfinite Dimensional Analysis, Quantum Probability and Related Topics, 03
A. Vershik, N. Tsilevich (2003)
Fock factorizations, and decompositions of the L2 spaces over general Lévy processesRussian Mathematical Surveys, 58
E. Lytvynov (1995)
Multiple Wiener integrals and non-Gaussian white noises: a Jacobi field approachMethods Funct. Anal. Topol., 1
Z. Huang, Xiaoshan Hu, Xiangjun Wang (2002)
Explicit forms of Wick tensor powers in general white noise spacesInternational Journal of Mathematics and Mathematical Sciences, 31
T. Hida (1975)
Analysis of Brownian Functionals, Carleton Math. Lect. Notes, Vol. 13
Y. Berezansky, D. Mierzejewski (2003)
THE CONSTRUCTION OF THE CHAOTIC REPRESENTATION FOR THE GAMMA FIELDInfinite Dimensional Analysis, Quantum Probability and Related Topics, 06
E. Lytvynov (2003)
Orthogonal decompositions for Lévy processes with an application to the gamma, Pascal and Meixner processesInfin. Dimens. Anal. Quantum Probab., 6
W. Schoutens (2000)
Stochastic Processes and Orthogonal Polynomials, Lect. Notes in Statistics, Vol. 146
E. Lytvynov, A. Rebenko, Gennadi Shchepan'ur (1997)
Wick calculus on spaces of generalized functions of compound poisson white noiseReports on Mathematical Physics, 39
J. Meixner (1934)
Orthogonale Polynomsysteme Mit Einer Besonderen Gestalt Der Erzeugenden FunktionJournal of The London Mathematical Society-second Series
A. M. Vershik, N. V. Tsilevich (2003)
Fock factorizations and decompositions of the L 2 spaces over general Lévy processesRuss. Math. Surv., 58
Y. Berezansky, E. Lytvynov, D. Mierzejewski (2003)
The Jacobi Field of a Lévy ProcessUkrainian Mathematical Journal, 55
Yuh-Jia Lee, Hsin-Hung Shih (1999)
The Segal-Bargmann transform for Levy functionalsJournal of Functional Analysis, 168
S. Albeverio, Yu.L. Daletsky, Y. Kondratiev, L. Streit (1996)
Non-Gaussian Infinite Dimensional AnalysisJournal of Functional Analysis, 138
L. Lerer, L. Rodman (1996)
Common Zero Structure of Rational Matrix FunctionsJournal of Functional Analysis, 136
A. Løkka (2004)
Martingale Representation of Functionals of Lévy ProcessesStochastic Analysis and Applications, 22
Yoshifusa Ito, I. Kubo (1988)
Calculus on Gaussian and Poisson white noisesNagoya Mathematical Journal, 111
T. Hida (1976)
ANALYSIS OF BROWNIAN FUNCTIONALS
I. Kubo (2004)
GENERATING FUNCTIONS OF EXPONENTIAL TYPE FOR ORTHOGONAL POLYNOMIALSInfinite Dimensional Analysis, Quantum Probability and Related Topics, 07
Eugene Lytvynov, Eugene Lytvynov (2002)
Polynomials of Meixner's type in infinite dimensions-Jacobi fields and orthogonality measuresJournal of Functional Analysis, 200
D. Surgails (1984)
On multiple Poisson stochastic integrals and associated Markov semigroupsProbab. Math. Stat., 3
Y. Kondratiev, José Silva, L. Streit, G. Us (1999)
Analysis on Poisson and Gamma spacesInfinite Dimensional Analysis, Quantum Probability and Related Topics, 01
R. Hudson, K. Parthasarathy (1984)
Quantum Ito's formula and stochastic evolutionsCommunications in Mathematical Physics, 93
G. Nunno, B. Øksendal, F. Proske (2004)
White Noise Analysis for Lévy Processes.Journal of Functional Analysis, 206
Kiyosi Itô (1956)
SPECTRAL TYPE OF THE SHIFT TRANSFORMATION OF DIFFERENTIAL PROCESSES WITH STATIONARY INCREMENTS(Transactions of the American Mathematical Society, 81
D. Nualart, W. Schoutens (2000)
Chaotic and predictable representation for L'evy Processes
E. Lytvynov (2002)
Orthogonal decompositions for L?evy processes with an application to the gamma
W. Schoutens (2000)
Stochastic processes and orthogonal polynomials
Consider the Lévy white noise space $${\left( {{\user1{\mathcal{S}}}*,\mu } \right)}$$ where $${\user1{\mathcal{S}}}*$$ is the space of Schwartz tempered distributions over $$\mathbb{R}^{d} $$ and μ is a Lévy white noise measure lifted from a one-dimensional infinitely divisible distribution with finite moments. The classical polynomials of Meixner's type are distinguished through a special form of their generating functions. By lifting the generating function of Meixner orthogonal polynomials, we construct the renormalization kernels explicitly in a unified way. Moreover, we define inner products in n-particle spaces in terms of traces on the ‘diagonals’ and obtain a unified explicit chaotic representation of Lévy–Meixner white noise functionals in terms of interacting Fock spaces. The interacting feature is completely determined by a function g which is referred to as ‘interaction exponent’. This method enables us to easily recapture the general form of Lévy–Meixner field operators.
Acta Applicandae Mathematicae – Springer Journals
Published: Oct 11, 2005
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