Product and Moment Formulas for Iterated Stochastic Integrals (associated with L\'evy Processes)

TL;DR

This paper derives explicit product and moment formulas for iterated stochastic integrals related to Le9vy processes, using a novel approach based on compensated-covariation stable families of martingales.

Contribution

It introduces a new method applying compensated-covariation stable families to obtain formulas for iterated integrals of Le9vy processes, encompassing jumps and Gaussian components.

Findings

Explicit product formulas for iterated integrals

Moment formulas for integrals involving Le9vy processes

Applicable to processes with jumps and Gaussian parts

Abstract

In this paper, we obtain explicit product and moment formulas for products of iterated integrals generated by families of square integrable martingales associated with an arbitrary L\'evy process. We propose a new approach applying the theory of compensated-covariation stable families of martingales. Our main tool is a representation formula for products of elements of a compensated-covariation stable family, which enables to consider L\'evy processes, with both jumps and Gaussian part.