On Itô formulas for jump processes

István Gyöngy () and Sizhou Wu ()
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István Gyöngy: University of Edinburgh, Scotland
Sizhou Wu: University of Edinburgh

Queueing Systems: Theory and Applications, 2021, vol. 98, issue 3, No 4, 247-273

Abstract: 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.

Keywords: Itô formula; Random measures; Lévy processes; Primary 60H05; 60H15; Secondary 35R60; 60H30 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11134-021-09709-8

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