Local characteristics and tangency of vector-valued martingales

Local characteristics and tangency of vector-valued martingales

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...

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Veröffentlicht in:arXiv.org 2020-09
1. Verfasser: Yaroslavtsev, Ivan S
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Banach spaces
Martingales
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description 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, Kwapie\'{n}, McConnell, and Woyczy\'{n}ski. The vast majority of the assertions presented in the paper is done under the sufficient and necessary UMD assumption on the corresponding Banach space.
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subjects Banach spaces
Martingales
title Local characteristics and tangency of vector-valued martingales
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