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On Itô formulas for jump processes

Author

Listed:
  • István Gyöngy

    (University of Edinburgh, Scotland)

  • Sizhou Wu

    (University of Edinburgh)

Abstract

A well-known Itô formula for finite-dimensional processes, given in terms of stochastic integrals with respect to Wiener processes and Poisson random measures, is revisited and is revised. The revised formula, which corresponds to the classical Itô formula for semimartingales with jumps, is then used to obtain a generalisation of an important infinite-dimensional Itô formula for continuous semimartingales from Krylov (Probab Theory Relat Fields 147:583–605, 2010) to a class of $$L_p$$ L p -valued jump processes. This generalisation is motivated by applications in the theory of stochastic PDEs.

Suggested Citation

  • István Gyöngy & Sizhou Wu, 2021. "On Itô formulas for jump processes," Queueing Systems: Theory and Applications, Springer, vol. 98(3), pages 247-273, August.
    • Handle: RePEc:spr:queues:v:98:y:2021:i:3:d:10.1007_s11134-021-09709-8
    DOI: 10.1007/s11134-021-09709-8
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