Open Access
2020 Local characteristics and tangency of vector-valued martingales
Ivan S. Yaroslavtsev
Probab. Surveys 17: 545-676 (2020). DOI: 10.1214/19-PS337


This paper is devoted to tangent martingales in Banach spaces. We provide the definition of tangency through local characteristics, basic $L^{p}$- and $\phi $-estimates, a precise construction of a decoupled tangent martingale, 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 results in this direction e.g. due to Grigelionis, Hitczenko, Jacod, Kallenberg, Kwapień, McConnell, and Woyczyński. The vast majority of the assertions presented in the paper is done under the necessary and sufficient UMD assumption on the corresponding Banach space.


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Ivan S. Yaroslavtsev. "Local characteristics and tangency of vector-valued martingales." Probab. Surveys 17 545 - 676, 2020.


Received: 1 August 2019; Published: 2020
First available in Project Euclid: 2 October 2020

Digital Object Identifier: 10.1214/19-PS337

Primary: 60B11 , 60G44
Secondary: 28A50 , ‎46G12 , 60G51 , 60G57 , 60H05

Keywords: Canonical decomposition , Decoupling , Independent increments , Lévy-Khinchin formula , local characteristics , stochastic integration , Tangent martingales , UMD Banach spaces

Vol.17 • 2020
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