Egghe, L.,
Stopping Time Techniques for Analysts and Probabilists / Stopping Time Techniques for Analysts & Probabilists L. Egghe. - Cambridge : Cambridge University Press, 1984. - 1 online resource (368 pages) : digital, PDF file(s). - London Mathematical Society Lecture Note Series ; no. 100 . - London Mathematical Society Lecture Note Series ; no. 100. .
Title from publisher's bibliographic system (viewed on 16 Oct 2015).
This book considers convergence of adapted sequences of real and Banach space-valued integrable functions, emphasizing the use of stopping time techniques. Not only are highly specialized results given, but also elementary applications of these results. The book starts by discussing the convergence theory of martingales and sub-( or super-) martingales with values in a Banach space with or without the Radon-Nikodym property. Several inequalities which are of use in the study of the convergence of more general adapted sequence such as (uniform) amarts, mils and pramarts are proved and sub- and superpramarts are discussed and applied to the convergence of pramarts. Most of the results have a strong relationship with (or in fact are characterizations of) topological or geometrical properties of Banach spaces. The book will interest research and graduate students in probability theory, functional analysis and measure theory, as well as proving a useful textbook for specialized courses on martingale theory.
9780511526176 (ebook)
Martingales (Mathematics)
Convergence
QA274.5 / .E37 1984
519.2/87
Stopping Time Techniques for Analysts and Probabilists / Stopping Time Techniques for Analysts & Probabilists L. Egghe. - Cambridge : Cambridge University Press, 1984. - 1 online resource (368 pages) : digital, PDF file(s). - London Mathematical Society Lecture Note Series ; no. 100 . - London Mathematical Society Lecture Note Series ; no. 100. .
Title from publisher's bibliographic system (viewed on 16 Oct 2015).
This book considers convergence of adapted sequences of real and Banach space-valued integrable functions, emphasizing the use of stopping time techniques. Not only are highly specialized results given, but also elementary applications of these results. The book starts by discussing the convergence theory of martingales and sub-( or super-) martingales with values in a Banach space with or without the Radon-Nikodym property. Several inequalities which are of use in the study of the convergence of more general adapted sequence such as (uniform) amarts, mils and pramarts are proved and sub- and superpramarts are discussed and applied to the convergence of pramarts. Most of the results have a strong relationship with (or in fact are characterizations of) topological or geometrical properties of Banach spaces. The book will interest research and graduate students in probability theory, functional analysis and measure theory, as well as proving a useful textbook for specialized courses on martingale theory.
9780511526176 (ebook)
Martingales (Mathematics)
Convergence
QA274.5 / .E37 1984
519.2/87