Stopping time techniques for analysts and probabilists / L. Egghe.
Material type:
TextSeries: London Mathematical Society lecture note series ; 100.Publication details: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1984. Description: 1 online resource (xvi, 351 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9781107361324; 110736132XSubject(s): Martingales (Mathematics) | Convergence | MATHEMATICS -- Probability & Statistics -- General | Convergence | Martingales (Mathematics) | Funktionalanalysis | Konvergenz | Martingal | Wahrscheinlichkeitsrechnung | Waarschijnlijkheid (statistiek) | Convergentie (wiskunde) | Martingales (mathématiques) | Convergence (mathématiques) | Funktionalanalysis | Konvergenz | Martingal | WahrscheinlichkeitsrechnungGenre/Form: Electronic books. | Electronic books. Additional physical formats: Print version:: Stopping time techniques for analysts and probabilists.DDC classification: 519.2/87 LOC classification: QA274.5 | .E37 1984ebOther classification: 31.70 | 31.46 Online resources: Click here to access online Summary: 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.
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Includes bibliographical references (pages 333-343) and index.
Print version record.
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.