Local characteristics and tangency of vector-valued martingales

Ivan S. Yaroslavtsev

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
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Abstract

This paper is devoted to tangent martingales in Banach spaces. We provide the definition of tangency through local characteristics, basic Lp- and ø-estimates, a precise construction of a decoupled tangent martin-gale, new estimates for vector-valued stochastic integrals, and several other claims concerning tangent martingales and local characteristics in infinite dimensions. This work extends various real-valued and vector-valued re-sults in this direction e.g. due to Grigelionis, Hitczenko, Jacod, Kallenberg, Kwapien, McConnell, and Woyczynski. The vast majority of the assertions presented in the paper is done under the necessary and sufficient UMD assumption on the corresponding Banach space.

Original languageEnglish
Pages (from-to)545-676
Number of pages132
JournalProbability Surveys
Volume17
DOIs
Publication statusPublished - 2020

Keywords

  • canonical decomposition
  • decoupling
  • independent increments
  • Levy-Khinchin formula
  • local charac-teristics
  • stochastic integra-tion
  • Tangent martingales
  • UMD Banach spaces

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