Gamma Noise Analysis

1997/02/11 by A. V. Gorbunov, Gorbunov, A. V., G. F. Us +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Functional Analysis (math.FA) #Probability (math.PR) #Stochastic processes and financial applications #funct-an #math.FA #math.PR

paper · pdf · doi:10.48550/arxiv.funct-an/9702005

4 pages, AMSTeX, to appear in Proceedings of the Seventh Crimean Autumn Mathematical School-Simposium on Spectral and Evolutionary Problems (September, 18-29, 1996, Sevastopol, Ukraine)

arxiv created 1997/02/11 · openalex publication_date 1997/02/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study an infinite dimensional analysis with respect to the measure on Schwartz space of tempered distributions, corresponding to the distributional derivative of gamma process. Laguerre polynomials being orthogonal with respect to gamma noise measure turn out to be generalized Appell ones. This fact enables to generalize the white noise functional approach on the stochastic Wick-Skorokhod equations involving gamma noise. E. g. we consider Werhulst type equation driven by gamma noise.

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