Local characteristics and tangency of vector-valued martingales

Journal article (2020)

Authors

I.S. Yaroslavtsev Max Planck Institute for Mathematics in the Sciences, Analysis - EEMCS
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2020 I.S. Yaroslavtsev
DOI: https://doi.org/10.1214/19-PS337
UMD Banach spaces Decoupling Canonical decomposition Independent increments Levy-Khinchin formula Local charac-teristics Stochastic integra-tion Tangent martingales
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Published Date

2020

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

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.