Cylindrical fractional Brownian motion in Banach spaces

E. Issoglio and M. Riedle

Stochastic Processes and their Applications, 2014, vol. 124, issue 11, 3507-3534

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–Loève 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.

Keywords: Cylindrical fractional Brownian motion; Stochastic integration in Banach spaces; Stochastic partial differential equations; Fractional Ornstein–Uhlenbeck process; γ-radonifying; Cylindrical measures (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:124:y:2014:i:11:p:3507-3534

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DOI: 10.1016/j.spa.2014.05.010

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