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Titlebook: Probability Theory; An Advanced Course Vivek S. Borkar Textbook 1995 Springer Science+Business Media New York 1995 Markov chain.Markov prop

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發(fā)表于 2025-3-21 17:19:05 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Probability Theory
副標題An Advanced Course
編輯Vivek S. Borkar
視頻videohttp://file.papertrans.cn/757/756892/756892.mp4
叢書名稱Universitext
圖書封面Titlebook: Probability Theory; An Advanced Course Vivek S. Borkar Textbook 1995 Springer Science+Business Media New York 1995 Markov chain.Markov prop
描述This book presents a selection of topics from probability theory. Essentially, the topics chosen are those that are likely to be the most useful to someone planning to pursue research in the modern theory of stochastic processes. The prospective reader is assumed to have good mathematical maturity. In particular, he should have prior exposure to basic probability theory at the level of, say, K.L. Chung‘s ‘Elementary probability theory with stochastic processes‘ (Springer-Verlag, 1974) and real and functional analysis at the level of Royden‘s ‘Real analysis‘ (Macmillan, 1968). The first chapter is a rapid overview of the basics. Each subsequent chapter deals with a separate topic in detail. There is clearly some selection involved and therefore many omissions, but that cannot be helped in a book of this size. The style is deliberately terse to enforce active learning. Thus several tidbits of deduction are left to the reader as labelled exercises in the main text of each chapter. In addition, there are supplementary exercises at the end. In the preface to his classic text on probability (‘Probability‘, Addison- Wesley, 1968), Leo Breiman speaks of the right and left hands of probabil
出版日期Textbook 1995
關(guān)鍵詞Markov chain; Markov property; Martingale; Operations Research; Probability theory; Random variable; Stoch
版次1
doihttps://doi.org/10.1007/978-1-4612-0791-7
isbn_softcover978-0-387-94558-3
isbn_ebook978-1-4612-0791-7Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer Science+Business Media New York 1995
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Conditioning and Martingales,ility of . given (or, equivalently, “conditioned on”) B”. The words “given . ” imply prior knowledge of the fact that the sample point ω lies in . It is then natural to consider the reduced probability space (Ω, ., .) with Ω. = . = A∩B . ∈ . (the “trace σ-field”), .(C) = P(C)/P(B) for . ∈ ., and def
地板
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Markov Chains,of integers or reals. I has the interpretation of a (discrete or continuous) time interval, . thereby being a time index. The simplest random process in discrete time is a sequence of independent random variables. This can be considered as a process without memory: the value of the process at a give
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Vivek S. Borkarocrat- or Republican-leaning, or in continuous scales ranging from most liberal to most conservative. Recent studies have stressed the need for studying these phenomena in complex social networks in additional dimensions of social cleavage, including anti-elite polarization and attitudes towards cha
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發(fā)表于 2025-3-22 17:39:14 | 只看該作者
Vivek S. Borkartion, analysis and applications of software, ontology, and c.This book provides a comprehensive review of complex networks from three different domains, presents novel methods for analyzing them, and highlights applications with accompanying case studies. Special emphasis is placed on three specific
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發(fā)表于 2025-3-22 21:15:59 | 只看該作者
Vivek S. Borkartion, analysis and applications of software, ontology, and c.This book provides a comprehensive review of complex networks from three different domains, presents novel methods for analyzing them, and highlights applications with accompanying case studies. Special emphasis is placed on three specific
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發(fā)表于 2025-3-23 02:37:52 | 只看該作者
Vivek S. Borkarmetrics which generalize K?hler Ricci-flat metrics to the non-K?hler setting. These non-K?hler Calabi–Yau manifolds have their origins in theoretical physics, where they were introduced in the works of C. Hull and A. Strominger. We will introduce tools from geometric analysis, namely geometric flows
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發(fā)表于 2025-3-23 06:31:19 | 只看該作者
Vivek S. Borkarmetrics which generalize K?hler Ricci-flat metrics to the non-K?hler setting. These non-K?hler Calabi–Yau manifolds have their origins in theoretical physics, where they were introduced in the works of C. Hull and A. Strominger. We will introduce tools from geometric analysis, namely geometric flows
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