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Titlebook: Probability via Expectation; Peter Whittle Textbook 2000Latest edition Springer Science+Business Media New York 2000 Markov process.Marti

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发表于 2025-3-21 17:58:41 | 显示全部楼层 |阅读模式
书目名称Probability via Expectation
编辑Peter Whittle
视频video
丛书名称Springer Texts in Statistics
图书封面Titlebook: Probability via Expectation;  Peter Whittle Textbook 2000Latest edition Springer Science+Business Media New York  2000 Markov process.Marti
描述The third edition of 1992 constituted a major reworking of the original text, and the preface to that edition still represents my position on the issues that stimulated me first to write. The present edition contains a number of minor modifications and corrections, but its principal innovation is the addition of material on dynamic programming, optimal allocation, option pricing and large deviations. These are substantial topics, but ones into which one can gain an insight with less labour than is generally thought. They all involve the expectation concept in an essential fashion, even the treatment of option pricing, which seems initially to forswear expectation in favour of an arbitrage criterion. I am grateful to readers and to Springer-Verlag for their continuing interest in the approach taken in this work. Peter Whittle Preface to the Third Edition This book is a complete revision of the earlier work Probability which appeared in 1970. While revised so radically and incorporatingso much new material as to amount to a new text, it preserves both the aim and the approach of the original. That aim was stated as the provision of a ‘first text in probability, demanding a reasonable
出版日期Textbook 2000Latest edition
关键词Markov process; Martingale; Probability Theory; Random variable; optimization; probability measure
版次4
doihttps://doi.org/10.1007/978-1-4612-0509-8
isbn_softcover978-1-4612-6795-9
isbn_ebook978-1-4612-0509-8Series ISSN 1431-875X Series E-ISSN 2197-4136
issn_series 1431-875X
copyrightSpringer Science+Business Media New York 2000
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发表于 2025-3-21 22:58:35 | 显示全部楼层
Expectation,of .. The description of the variation of ω over Ω implied by the specification of these expectations will be termed a . or .. The introduction of a probabilistic element justifies the term ., which we shall consistently abbreviate to r.v.
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发表于 2025-3-22 07:33:46 | 显示全部楼层
Large-Deviation Theory,n so many applications. Roughly, it applies to systems that have a large-scale character (in a sense to be defined) and exploits this scale to derive the essential stochastic behaviour of the system, although without going all the way to the deterministic limit.
发表于 2025-3-22 11:21:00 | 显示全部楼层
The Two Basic Limit Theorems,tation. There is then interest in confirming whether such behaviour can be reproduced within the theory, in that one can demonstrate convergence of . in some well-defined sense, under appropriate assumptions.
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发表于 2025-3-22 18:49:35 | 显示全部楼层
1431-875X n the issues that stimulated me first to write. The present edition contains a number of minor modifications and corrections, but its principal innovation is the addition of material on dynamic programming, optimal allocation, option pricing and large deviations. These are substantial topics, but on
发表于 2025-3-22 23:41:30 | 显示全部楼层
发表于 2025-3-23 03:54:58 | 显示全部楼层
Stochastic Convergence,e encounter should be construed as a limit, in some sense, of a finite sum. Consider, for instance, the sum 282-2 of Section 6.1, or the formal solution 282-3 of the stochastic difference equation 282-4.
发表于 2025-3-23 06:03:49 | 显示全部楼层
Probability,’ or ‘the patient survives’. As we saw in Section 2.3, the formal characterization of the event is as a set of realizations ω, i.e. a subset of Ω, also denoted by .. This is just the set of realizations for which the event occurs.
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