A comparison principle for stochastic integro-differential equations

TL;DR

This paper establishes a comparison principle for stochastic integro-differential equations driven by Levy processes, extending an Ito formula to handle discontinuous semimartingales, which advances the theoretical understanding of such equations.

Contribution

It introduces a novel comparison principle for stochastic integro-differential equations driven by Levy processes, extending Ito's formula to discontinuous semimartingales.

Findings

Proved a comparison principle for Levy-driven stochastic integro-differential equations.

Extended Ito's formula to discontinuous semimartingales.

Provides a theoretical tool for analyzing solutions of such equations.

Abstract

A comparison principle for stochastic integro-differential equations driven by Levy processes is proved. This result is obtained via an extension of an Ito formula from [11] for the square of the norm of the positive part of $L_2-$valued, continuous semimartingales, to the case of discontinuous semimartingales.