Gamma Noise Analysis

TL;DR

This paper develops an infinite dimensional analysis framework for gamma noise, extending white noise functional methods to stochastic equations driven by gamma processes, including a Werhulst type model.

Contribution

It introduces a gamma noise measure on Schwartz space and generalizes Appell polynomials, enabling analysis of stochastic equations with gamma noise.

Findings

Orthogonal polynomials are generalized Appell polynomials.

White noise functional approach is extended to gamma noise.

Application to Werhulst type stochastic equations.

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.