Cylindrical Wiener processes

Riedle, Markus (2008) Cylindrical Wiener processes. [MIMS Preprint]

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Abstract

In this work cylindrical Wiener processes on Banach spaces are defined by means of cylindrical stochastic processes, which are a well considered mathematical object. This approach allows a definition which is a simple straightforward extension of the real-valued situation. We apply this definition to introduce a stochastic integral with respect to cylindrical Wiener processes. Again, this definition is a straightforward extension of the real-valued situation which results now in simple conditions on the integrand. In particular, we do not have to put any geometric constraints on the Banach space under consideration. Finally, we relate this integral to well-known stochastic integrals in literature.

Item Type: MIMS Preprint
Uncontrolled Keywords: cylindrical processes; cylindrical measures; stochastic integral; stochastic differential equations
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User: Dr Markus Riedle
Date Deposited: 15 Feb 2008
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1043

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