A chaotic decomposition for generalized stochastic processes with independent values

TL;DR

This paper extends the chaotic decomposition framework from Lévy processes to a broader class of generalized stochastic processes with independent values, enhancing the mathematical tools available for analyzing such processes.

Contribution

It introduces a chaotic decomposition for generalized stochastic processes with independent values, generalizing previous results for Lévy processes.

Findings

Established a chaotic decomposition for generalized stochastic processes with independent values.

Extended the mathematical framework for analyzing complex stochastic processes.

Provided tools for future research in stochastic analysis and applications.

Abstract

We extend the result of Nualart and Schoutens on chaotic decomposition of the $L^2$-space of a L\'evy process to the case of a generalized stochastic processes with independent values.