Stopping time techniques for analysts and probabilists /

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Egghe, L. (Leo)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1984.
Colección:London Mathematical Society lecture note series ; 100.
Temas:
Martingales (Mathematics)
Convergence.
Martingales (Mathématiques)
Convergence (Mathématiques)
MATHEMATICS > Probability & Statistics > General.
Funktionalanalysis
Konvergenz
Martingal
Wahrscheinlichkeitsrechnung
Waarschijnlijkheid (statistiek)
Convergentie (wiskunde)
Martingales (mathématiques)
Convergence (mathématiques)
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover; Title; Copyright; Contents; Preface; Chapter I : Types of convergence; I.1. Introduction; I.1.1. Measurable functions; I.1.2. Integrable functions; I.2. Adapted sequences; I.2.1. Definition; I.2.2. Conditional expectations; I.3. Convergence; I.3.1. Pointwise convergence; I.3.2. Mean convergence; I.3.3. Pettis convergence; I.3.4. Convergence in probability; I.3.5. Convergence in probability in the stopping time sense; I.4. Notes and remarks; Chapter II : Martingale convergence theorems; II. 1. Elementary results; II. 2. Main results
  • II. 3. Convergence of martingales in general Banach spacesII. 4. Notes and remarks; Chapter III : Sub- and supermartingale convergence theorems; III. 1. Preliminary results; III. 2. Heinich's theorem on the convergence of positive submartingales; III. 3. Convergence of general submartingales; III. 4. Convergence of supermartingales; III. 5. Submartingale convergence in Banach lattices without (RNP); III. 6. Notes and remarks; Chapter IV : Basic inequalities for adapted sequences; IV. 1. Basic inequalities; IV. 2. Failure of the inequalities; IV. 3. Notes and remarks
  • Chapter V : Convergence of generalized martingales in Banach spaces
  • the mean wayV. I. Uniform amarts; V.2. Amarts; V.3. Weak sequential amarts; V.4. Weak amarts; V.5. Semiamarts; V.6. Notes and remarks; Chapter VI : General directed index sets and applications of amart theory; VI. 1. Convergence of adapted nets; VI. 2. Applications of amart convergence results; VI. 3. Notes and remarks; Chapter VII : Disadvantages of amarts. Convergence of generalized martingales in Banach spaces
  • the pointwise way; VII. 1. Disadvantages of amarts; VII. 2. Pramarts, mils, GFT; VII. 3. Notes and remarks
  • Chapter VIII : Convergence of generalized sub- and supermartingales in Banach latticesVIII. 1. Subpramarts, superpramarts and related notions; VIII. 2. Applications to pramartconvergence; VIII. 3. Notes and remarks; Chapter IX : Closing remarks; IX. 1. A general remark concerning scalar convergence; IX. 2. Summary of the most important convergence results; IX. 3. Convergence of adapted sequences of Pettis integrable functions; References; List of notations; Subject index

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