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A Comparison Principle for Stochastic Integro-Differential Equations

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Abstract

A comparison principle for stochastic integro-differential equations driven by Lévy processes is proved. This result is obtained via an extension of an Itô formula, proved by N.V. Krylov, for the square of the norm of the positive part of L 2 − valued, continuous semimartingales, to the case of discontinuous semimartingales.

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Authors and Affiliations

  1. School of Mathematics University of Edinburgh King’s Buildings Edinburgh, Edinburgh, UK

    Konstantinos Anastasios Dareiotis & István Gyöngy

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  1. Konstantinos Anastasios Dareiotis
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  2. István Gyöngy
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Correspondence to Konstantinos Anastasios Dareiotis.

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Dareiotis, K.A., Gyöngy, I. A Comparison Principle for Stochastic Integro-Differential Equations. Potential Anal 41, 1203–1222 (2014). https://doi.org/10.1007/s11118-014-9416-7

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  • DOI: https://doi.org/10.1007/s11118-014-9416-7

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