ON IT^O FORMULAS FOR JUMP PROCESSES

Istvan Gyongy; Sizhou Wu

ON IT^O FORMULAS FOR JUMP PROCESSES

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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 Lp-valued jump processes. This generalisation is motivated by applications in the theory of stochastic PDEs.

Original language	English
Number of pages	22
Journal	Queueing Systems
Publication status	Accepted/In press - 30 Jun 2021

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https://arxiv.org/abs/2007.14782

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title = "ON IT^O FORMULAS FOR JUMP PROCESSES",

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 Lp-valued jump processes. This generalisation is motivated by applications in the theory of stochastic PDEs. ",

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T1 - ON IT^O FORMULAS FOR JUMP PROCESSES

AU - Gyongy, Istvan

AU - Wu, Sizhou

PY - 2021/6/30

Y1 - 2021/6/30

N2 - 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 Lp-valued jump processes. This generalisation is motivated by applications in the theory of stochastic PDEs.

AB - 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 Lp-valued jump processes. This generalisation is motivated by applications in the theory of stochastic PDEs.

M3 - Article

JO - Queueing Systems

JF - Queueing Systems

SN - 0257-0130

ER -

ON IT^O FORMULAS FOR JUMP PROCESSES

Abstract

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