On It\^o formulas for jump processes
Probability
2020-07-30 v1
Abstract
A well-known It\^o 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 It\^o formula for semimartingales with jumps, is then used to obtain a generalisation of an important infinite dimensional It\^o formula for continuous semimartingales proved by Krylov to a class of -valued jump processes. This generalisation is motivated by applications in the theory of stochastic PDEs.
Cite
@article{arxiv.2007.14782,
title = {On It\^o formulas for jump processes},
author = {István Gyöngy and Sizhou Wu},
journal= {arXiv preprint arXiv:2007.14782},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1904.12898