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arXiv · 1605.06946

Brownian representations of cylindrical continuous local martingales

Ivan S. Yaroslavtsev
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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 $M$ there exists a time change $τ$ such that $M\circ τ$ is Brownian representable.

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Ivan S. Yaroslavtsev. 2017-06-22. Brownian representations of cylindrical continuous local martingales. https://doi.org/10.1142/s0219025718500133

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