On Itô formulas for jump processes

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 proved by Krylov to a class of $L_p$-valued jump processes. This generalisation is motivated by applications in the theory of stochastic PDEs.

arXiv admin note: text overlap with arXiv:1904.12898

References in corpus (2)

• On $L_p$-Solvability of Stochastic Integro-Differential Equations
• Itô's formula for jump processes in $L_p$-spaces