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 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...

Martingales and stochastic calculus in Banach spaces

In this thesis we study martingales and stochastic integration of processes with<br/>values in UMD Banach spaces.

Martingale decompositions and weak differential subordination in UMD Banach spaces

In this paper, we consider Meyer–Yoeurp decompositions for UMD Banach space-valued martingales. Namely, we prove that X is a UMD Banach space if and only if for any fixed p ∈ (1, ∞), any X-valued L^p-martingale M has a unique decomposition M = M^d + M^c such that M^d is a purely discontinuous martingale...