Local characteristics and tangency of vector-valued martingales

Ivan S. Yaroslavtsev

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arXiv · 1907.11588

Local characteristics and tangency of vector-valued martingales

Ivan S. Yaroslavtsev

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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 $L^p$- 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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Ivan S. Yaroslavtsev. 2019-07-26. Local characteristics and tangency of vector-valued martingales. https://arxiv.org/abs/1907.11588

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