Brownian representations of cylindrical continuous local martingales

Ivan Yaroslavtsev

doi:10.1142/S0219025718500133

Brownian representations of cylindrical continuous local martingales

Ivan Yaroslavtsev^*

^*Corresponding author for this work

Analysis

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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.

Original language	English
Article number	1850013
Pages (from-to)	1-25
Number of pages	25
Journal	Infinite Dimensional Analysis, Quantum Probability and Related Topics
Volume	21
Issue number	2
DOIs	https://doi.org/10.1142/S0219025718500133
Publication status	Published - 2018

Keywords

Brownian representation
cylindrical martingale
quadratic variation
UMD spaces

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10.1142/S0219025718500133

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title = "Brownian representations of cylindrical continuous local martingales",

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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AB - 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.

KW - Brownian representation

KW - cylindrical martingale

KW - quadratic variation

KW - UMD spaces

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DO - 10.1142/S0219025718500133

M3 - Article

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JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics

IS - 2

M1 - 1850013

ER -

Brownian representations of cylindrical continuous local martingales

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Martingales and stochastic calculus in Banach spaces

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