UID:
edoccha_9958116502902883
Format:
1 online resource (245 p.)
Edition:
1st ed.
ISBN:
1-282-30920-X
,
9786612309205
,
0-08-095418-9
Series Statement:
North-Holland mathematical library
Content:
This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field.
Note:
Description based upon print version of record.
,
Front Cover; Discrete-Parameter Martingales; Copyright Page; Table of Contents; Preface; Chapter I Preliminaries on conditional expectations; I-1 Sub-s-fields of a probability space; I-2 Conditional expectations; I-3 Supplement: Conditional expectations with respect to a s finite measure; Chapter II Positive martingales and supermartingales; II-1 Stopping times; II-2 Positive supermartingales; II-3 Exercises; Chapter III Applications; III-1 Positive martingales and set functions. The Lebesgue and Radon-Nikodym theorems on the decomposition of measures; III-2 Applications to statistical tests
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III-3 Haar systems and basesIII-4 Gaussian spaces; III-5 Application to Markov chains; Chapter IV Convergence and regularity of martingales; IV-1 A.s. convergence of Submartingales; IV-2 Regularity of integrable martingales; IV-3 Regular stopping times for an integrable martingale; IV-4 Application: An exponential formula and Wald's identity; IV-5 Supplements; IV-6 Exercises; Chapter V Extensions of the notion of martingale; V-1 Martingales with a directed index set; V-2 Vector-valued martingales; V-3 Reversed martingales; Chapter VI Optimisation problems; VI-1 Snell's problem
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VI-2 Application to Markov chainsVI-3 Applications to random walks; VI-4 Another application; VI-5 Application to sequential statistical analysis; VI-6 A stochastic game; Chapter VII Doob's decomposition of submartingales and its application to square-integrable martingales; VII-1 Generalities; VII-2 Asymptotic behaviour of a square integrable martingale; VII-3 Martingales with integrable pth power; VII-4 Gundy's condition; VII-5 Exercises; Chapter VIII Doob's decomposition of positive supermartingales; VIII-1 Generalities; VIII-2 Supplement: A remarkable duality; VIII-3 Quadratic variation
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VIII-4 Martingale transformsVIII-5 Exercises; Appendix On the use of young's functions in the theory of martingales; A-1 Young's functions; A-2 Orlicz spaces; A-3 Applications to the theory of martingales; References; Index of terminology and notation
,
English
Additional Edition:
ISBN 0-7204-2810-6
Language:
English
