Brownian representations of cylindrical continuous local martingales
Journal Article
(2018)
Author(s)
I.S. Yaroslavtsev (TU Delft - Analysis)
Research Group
Analysis
DOI related publication
https://doi.org/10.1142/S0219025718500133
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https://resolver.tudelft.nl/uuid:e1074260-9f4c-4acd-905a-0991dbbba928
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Publication Year
2018
Language
English
Related content
Research Group
Analysis
Issue number
2
Volume number
21
Pages (from-to)
1-25
Abstract
In this paper, we give necessary and sufficient conditions for a cylindrical continuous local martingale to be the stochastic integral with respect to a cylindrical Brownian motion. In particular, we consider the class of cylindrical martingales with closed operator-generated covariations. We also prove that for every cylindrical continuous local martingale (Formula presented.) there exists a time change (Formula presented.) such that (Formula presented.) is Brownian representable.
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