Stochastic Integration for Levy Processes with Values in Banach Spaces

Riedle, Markus and van Gaans, Onno (2009) Stochastic Integration for Levy Processes with Values in Banach Spaces. Stochastic Processes and Applications, 119 (6). pp. 1952-1974. ISSN 0304-4149

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Official URL: http://dx.doi.org/10.1016/j.spa.2008.09.009

Abstract

A stochastic integral of Banach space valued deterministic functions with respect to Banach space valued Levy processes is defined. There are no conditions on the Banach spaces nor on the Levy processes. The integral is defined analogously to the Pettis integral. The integrability of a function is characterized by means of a radonifying property of an integral operator associated to the integrand. The integral is used to prove a Levy-Ito decomposition for Banach space valued Levy processes and to study existence and uniqueness of solutions of stochastic Cauchy problems driven by Levy processes.

Item Type: Article
Uncontrolled Keywords: Banach space valued stochastic integral, Cauchy problem, Levy-Ito decomposition, Levy process, martingale valued measure, Pettis integral, radonifying operator
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User: Dr Markus Riedle
Date Deposited: 05 May 2009
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1263

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