Geometry and martingales in banach spaces - Woyczyński, Wojbor A. (Boca Raton: CRC Press, 2018)
This book provides a compact exposition of the results explaining the interrelations existing between the metric geometry of Banach spaces and the theory of martingales, and general random vectors with values in those Banach spaces. Geometric concepts such as dentability, uniform smoothness, uniform convexity, Beck convexity, etc. turn out to characterize asymptotic behavior of martingales with values in Banach spaces.
1. Preliminaries: Probability and geometry in Banach spaces -- 2. Dentability, Radon-Nikodym Theorem, and Mar- tingale Convergence Theorem -- 3. Uniform Convexity and Uniform Smoothness. -- 4. Spaces that do not contain c0 -- 5. Cotypes of Banach spaces -- 6. Spaces of Rademacher and stable types -- 7. Spaces of type 2 -- 8. Beck convexity -- 9. Marcinkiewicz-Zygmund Theorem in Banach spaces
Includes bibliographical references and index.
Keywords: Geometric Analysis; Martingales -- Mathematics; Banach Spaces