An Itō Formula in the Space of Tempered Distributions

Article Type

Research Article

Publication Title

Journal of Theoretical Probability

Abstract

We extend the Itō formula (Rajeev in From Tanaka’s formula to Ito’s formula: distributions, tensor products and local times, Springer, Berlin, 2001, Theorem 2.3) for semimartingales with paths that are right continuous and have left limits. We also comment on the local time process of such semimartingales. We apply the Itō formula to Lévy processes to obtain existence of solutions to certain classes of stochastic differential equations in the Hermite–Sobolev spaces.

First Page

510

Last Page

528

DOI

10.1007/s10959-015-0639-3

Publication Date

6-1-2017

Comments

Open Access, Green

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