Brownian representations of cylindrical continuous local martingales

Ivan 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 (Formula presented.) there exists a time change (Formula presented.) such that (Formula presented.) is Brownian representable.

Original languageEnglish
Article number1850013
Pages (from-to)1-25
Number of pages25
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Volume21
Issue number2
DOIs
Publication statusPublished - 2018

Keywords

  • Brownian representation
  • cylindrical martingale
  • quadratic variation
  • UMD spaces

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  • Martingales and stochastic calculus in Banach spaces

    Yaroslavtsev, I., 1 Mar 2019, 302 p.

    Research output: ThesisDissertation (TU Delft)

    Open Access
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