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- catalog abstract ""In this book the technique of stopping times is applied to prove convergence theorems for stochastic processes - in particular processes indexed by direct sets - and in sequential analysis. Applications of convergence theorems are seen in probability, analysis, and ergodic theory." "Almost everywhere, convergence and stochastic convergence of processes indexed by a directed set are studied, and solutions are given for problems left open in Krickeberg's theory for martingales and submartingales. The rewording of Vitali covering conditions in terms of stopping times establishes connections with the theory of stochastic processes and derivation. A study of martingales yields laws of large numbers for martingale differences, with application to "star-mixing" processes. Convergence of processes taking values in Banach spaces is related to geometric properties of these spaces. There is a self-contained section on operator ergodic theorems: the superadditive, Chacon-Ornstein, and Chacon theorems." "A recurrent theme of the book is the unification of martingale and ergodic theorems. One example is the use of a "three-function inequality," which is basic in all the one and many parameter results. A general principle is proved showing that in both theories all the multiparameter convergence theorems follow from one-parameter maximal and convergence theorems." "Requiring only a knowledge of basic measure theory, this book will be a valuable reference for students and researchers in probability theory, analysis, and statistics."--BOOK JACKET.".
- catalog contributor b3873039.
- catalog contributor b3873040.
- catalog created "1992.".
- catalog date "1992".
- catalog date "1992.".
- catalog dateCopyrighted "1992.".
- catalog description ""In this book the technique of stopping times is applied to prove convergence theorems for stochastic processes - in particular processes indexed by direct sets - and in sequential analysis. Applications of convergence theorems are seen in probability, analysis, and ergodic theory." "Almost everywhere, convergence and stochastic convergence of processes indexed by a directed set are studied, and solutions are given for problems left open in Krickeberg's theory for martingales and submartingales. The rewording of Vitali covering conditions in terms of stopping times establishes connections with the theory of stochastic processes and derivation. A study of martingales yields laws of large numbers for martingale differences, with application to "star-mixing" processes. Convergence of processes taking values in Banach spaces is related to geometric properties of these spaces. There is a self-contained section on operator ergodic theorems: the superadditive, Chacon-Ornstein, and Chacon theorems." "A recurrent theme of the book is the unification of martingale and ergodic theorems. One example is the use of a "three-function inequality," which is basic in all the one and many parameter results. A general principle is proved showing that in both theories all the multiparameter convergence theorems follow from one-parameter maximal and convergence theorems." "Requiring only a knowledge of basic measure theory, this book will be a valuable reference for students and researchers in probability theory, analysis, and statistics."--BOOK JACKET.".
- catalog description "Includes bibliographical references and index.".
- catalog extent "xii, 428 p. :".
- catalog identifier "0521350239".
- catalog isPartOf "Encyclopedia of mathematics and its applications ; v. 47".
- catalog issued "1992".
- catalog issued "1992.".
- catalog language "eng".
- catalog publisher "Cambridge ; New York : Cambridge University Press,".
- catalog subject "519.2/6 20".
- catalog subject "Convergence.".
- catalog subject "Martingales (Mathematics)".
- catalog subject "Martingales.".
- catalog subject "Probabilities.".
- catalog subject "QA273.43 .E34 1992".
- catalog title "Stopping times and directed processes / G.A. Edgar and Louis Sucheston.".
- catalog type "Maringal. swd".
- catalog type "text".