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概率論和隨機過程-第2版 版權信息
- ISBN：9787510044106
- 條形碼：9787510044106 ; 978-7-5100-4410-6
- 裝幀：一般膠版紙
- 冊數：暫無
- 重量：暫無
- 所屬分類：>
概率論和隨機過程-第2版 本書特色
凱羅勒夫編著的《概率論和隨機過程》是以作者在Princeton大學和Maryland大學的講義為藍本擴充而成，書中的內容正好可作為《概率論和隨機過程》課程一學年的獨立教材。這對于高年級的本科生、研究生和想要了解本科目基礎知識的科研人員都是相當有用的。本書文筆流暢，其中的概念和相關的結果都是生動豐富，并具有啟發性。每章末都包含難易不等的練習題。這本書已經被作者用作Princeton大學和Maryland高年級本科生和研究生學習該科目的一學期的教程。目次：（**部分）概率論：隨機變量及其分布；獨立試驗序列；勒貝格積分和數學期望；條件概率和期望；具有有限數狀態的馬爾科夫鏈；大數定理；測度的弱收斂；特征函數；極限定理；幾個有趣的問題;（第二部分）隨機過程：基本概念；條件期望和鞅；有限狀態空間的馬爾科夫鏈；廣泛意義上的平穩隨機過程；嚴格平穩隨機過程；廣義隨機過程；布朗運動；馬爾科夫過程和馬爾科夫族；隨機積分和Ito公式；隨機微分方程；Gibbs隨機域。
概率論和隨機過程-第2版 內容簡介
this book is primarily based on a one-year course that has been taught for a number of years at princeton university to advanced undergraduate and graduate students. during the last year a similar course has also been taught at the university of maryland. we would like to express our thanks to ms. sophie lucas and prof. rafael herrera who read the manuscript and suggested many corrections. we are particularly grateful to prof. boris gurevich for making many important sug-gestions on both the mathematical content and style. while writing this book， l. koralov was supported by a national sci-ence foundation grant （dms-0405152）. y. sinai was supported by a national science foundation grant （dms-0600996）.
概率論和隨機過程-第2版 目錄
part ⅰ probability theory
1 random variables and their distributions
1.1 spaces of elementary outcomes， a-algebras， and measures
1.2 expectation and variance of random variables on a discrete probability space
1.3 probability of a union of events
1.4 equivalent formulations of a-additivity， borel a-algebras and measurability
1.5 distribution functions and densities
1.6 problems
2 sequences of independent trials
2.1 law of large numbers and applications
2.2 de moivre-laplace limit theorem and applications
2.3 poisson limit theorem.
2.4 problems
3 lebesgue integral and mathematical expectation
3.1 definition of the lebesgue integral
1 random variables and their distributions
1.1 spaces of elementary outcomes， a-algebras， and measures
1.2 expectation and variance of random variables on a discrete probability space
1.3 probability of a union of events
1.4 equivalent formulations of a-additivity， borel a-algebras and measurability
1.5 distribution functions and densities
1.6 problems
2 sequences of independent trials
2.1 law of large numbers and applications
2.2 de moivre-laplace limit theorem and applications
2.3 poisson limit theorem.
2.4 problems
3 lebesgue integral and mathematical expectation
3.1 definition of the lebesgue integral
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