Brownian representations of cylindrical continuous local martingales

Journal article (2018)

Authors

I.S. Yaroslavtsev Analysis - EEMCS
Research Group
Analysis (EEMCS) (TU Delft)
UMD spaces Cylindrical martingale Quadratic variation Brownian representation
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Published Date

2018

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

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.