The Resource Stopping times and directed processes, G.A. Edgar and Louis Sucheston
Stopping times and directed processes, G.A. Edgar and Louis Sucheston
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The item Stopping times and directed processes, G.A. Edgar and Louis Sucheston represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Stopping times and directed processes, G.A. Edgar and Louis Sucheston represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 "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 "starmixing" processes. Convergence of processes taking values in Banach spaces is related to geometric properties of these spaces. There is a selfcontained section on operator ergodic theorems: the superadditive, ChaconOrnstein, and Chacon theorems." "A recurrent theme of the book is the unification of martingale and ergodic theorems. One example is the use of a "threefunction 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 oneparameter 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
 Language
 eng
 Extent
 xii, 428 pages
 Isbn
 9780521350235
 Label
 Stopping times and directed processes
 Title
 Stopping times and directed processes
 Statement of responsibility
 G.A. Edgar and Louis Sucheston
 Language
 eng
 Summary
 "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 "starmixing" processes. Convergence of processes taking values in Banach spaces is related to geometric properties of these spaces. There is a selfcontained section on operator ergodic theorems: the superadditive, ChaconOrnstein, and Chacon theorems." "A recurrent theme of the book is the unification of martingale and ergodic theorems. One example is the use of a "threefunction 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 oneparameter 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
 Cataloging source
 DLC
 http://library.link/vocab/creatorDate
 1949
 http://library.link/vocab/creatorName
 Edgar, Gerald A.
 Illustrations
 illustrations
 Index
 index present
 Literary form
 non fiction
 Nature of contents
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Sucheston, Louis
 Series statement
 Encyclopedia of mathematics and its applications
 Series volume
 v. 47
 http://library.link/vocab/subjectName

 Convergence
 Probabilities
 Martingales (Mathematics)
 Label
 Stopping times and directed processes, G.A. Edgar and Louis Sucheston
 Bibliography note
 Includes bibliographical references (pages [407]417) and indexes
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Control code
 24953192
 Dimensions
 25 cm
 Extent
 xii, 428 pages
 Isbn
 9780521350235
 Lccn
 91044388
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Other physical details
 illustrations
 System control number
 (WaOLN)1466945
 Label
 Stopping times and directed processes, G.A. Edgar and Louis Sucheston
 Bibliography note
 Includes bibliographical references (pages [407]417) and indexes
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Control code
 24953192
 Dimensions
 25 cm
 Extent
 xii, 428 pages
 Isbn
 9780521350235
 Lccn
 91044388
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Other physical details
 illustrations
 System control number
 (WaOLN)1466945
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/StoppingtimesanddirectedprocessesG.A.Edgar/ZS3Px3L2ShY/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/StoppingtimesanddirectedprocessesG.A.Edgar/ZS3Px3L2ShY/">Stopping times and directed processes, G.A. Edgar and Louis Sucheston</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>