AN ITÔ INTEGRAL FOR A TWO-SIDED LÉVY PROCESS

Authors

• Raluca Balan, University of OttawaFollow
• Jaime Garza, University of OttawaFollow

Abstract

In this article, we construct an Itô integral with respect to a two-sided finite-variance Lévy process {L(x)}x∈R, without a Gaussian component. Using Rosenthal inequality for discrete-time martingales, we give an estimate for the p-th moment of this integral, for any even integer p ≥ 2. Then, using Poisson-Malliavin calculus, we show that the Itô integral is an extension of the Hitsuda-Skorokhod integral with respect to the compensated Poisson random measure associated to the Lévy process.

Recommended Citation

Balan, Raluca and Garza, Jaime (2026) "AN ITÔ INTEGRAL FOR A TWO-SIDED LÉVY PROCESS," Journal of Stochastic Analysis: Vol. 7: No. 2, Article 1.
DOI: 10.31390/josa.7.1.01
Available at: https://repository.lsu.edu/josa/vol7/iss2/1

DOI

10.31390/josa.7.1.01