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A Comparison of Two Settings for Stochastic Integration with Respect to Lévy Processes in Infinite Dimensions

  • Justin Cyr
  • Sisi Tang
  • Roger TemamEmail author
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Part of the Springer INdAM Series book series (SINDAMS, volume 27)

Abstract

We review two settings for stochastic integration with respect to infinite dimensional Lévy processes. We relate notions of stochastic integration with respect to square-integrable Lévy martingales, compound Poisson processes, Poisson random measures and compensated Poisson random measures. We use the Lévy-Khinchin decomposition to decompose stochastic integrals with respect to general, non-square-integrable Lévy processes into a Riemann integral and stochastic integrals with respect to a Wiener process, Poisson random measure and compensated Poisson random measure. Besides its intrinsic interest this review article is also meant as a step toward new studies in stochastic partial differential equations with Lévy noise.

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Notes

Acknowledgements

This work was partially supported by the National Science Foundation (NSF) under the grant DMS-1510249 and by the Research Fund of Indiana University. The authors gratefully acknowledge the use of the book [15] during a semester-long seminar, and some private exchanges of emails with the authors.

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Authors and Affiliations

  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA

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