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Cylindrical Fractional Brownian Motion in Banach Spaces

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)3507-3534
Number of pages28
JournalStochastic Processes and Their Applications
Volume124
Issue number11
Early online date29 May 2014
DOIs
E-pub ahead of print29 May 2014
PublishedNov 2014

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Abstract

In this article we introduce cylindrical fractional Brownian motions in Banach spaces and develop the related stochastic integration theory. Here a cylindrical fractional Brownian motion is understood in the classical framework of cylindrical random variables and cylindrical measures. The developed stochastic integral for deterministic operator valued integrands is based on a series representation of the cylindrical fractional Brownian motion, which is analogous to the Karhunen-Lo\`eve expansion for genuine stochastic processes. In the last part we apply our results to study the abstract stochastic Cauchy problem in a Banach space driven by cylindrical fractional Brownian motion.

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