Cylindrical Fractional Brownian Motion in Banach Spaces
Probability
2015-11-19 v1
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.
Keywords
Cite
@article{arxiv.1307.4992,
title = {Cylindrical Fractional Brownian Motion in Banach Spaces},
author = {Elena Issoglio and Markus Riedle},
journal= {arXiv preprint arXiv:1307.4992},
year = {2015}
}
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29 pages