經典數學教材（影印版）：馬爾科夫過程、布朗運動和時間對稱（第2版） 下載 mobi epub pdf 電子書 2025

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內容簡介

　　This book consists of two parts， to be called Part I and Part n. Part I，Chapters l through 5， is essentially a new edition of Kai Lai Chung's Lec-tures from Markov Processes to Brownian Motion （1982）. He has corrected a number of misprints in the original edition， and has inserted a few references and remarks， of which he says， "The latter must be regarded as randomly selected since twenty-some years is a long time to retrace steps..." This part introduces strong Markov processes and their potential theory. In particular，it studies Brownian motion， and shows how it generates classical potential theory.

內頁插圖

目錄

Chapter 1 Markov Ptocess
1.1.Markov Property
1.2.Transition Function
1.3.Optional Times
1.4.Martingale Theorems
1.5.Progressive Measurability and the Section Theorem
Exercises
Notes on Chapter I

Chapter 2 Basic Properties
2.1. Martingale Connection
2.2.Feller Process
Exercises
2.3. Strong Markov Property and Right Continuity of Fields
Exercises
2.4. Moderate Markov Property and Quasi Left Continuity
Exercises
Notes on Chapter 2

Chapter 3 Hunt Process
3.1.Defining Properties
Exercises
3.2.Analysis of Excessive Functions
Exercises
3.3.Hitting Times
3.4.Balayage and Fundamental Structure
Exercises
3.5. FineProperties
Exercises
3.6.Decreasing Limits
Exercises
3.7.Recurrence and Transience
Exercises
3.8.Hypothesis (B)
Exerases
Notes on Chapter 3

Chapter 4 Brownian Motion
4.1.Spatial Homogeneity
Exercises
4.2.Preliminary Properties of Brownian Motion
Exercises
4.3.Harmonic Function
Exerases
4.4.Dirichlet Problem
Exercises
4.5.Superharmonic Function and Supermartingale
Exerases
4.6.The Role of the Laplacian
Exercises
4.7. The Feynman-Kac Functional and the Schrodinger Equation
Exe工ases
Notes on Chapter 4

Chapter 5 Potential Developments
5.1 Quitting Time and Equilibrium Measure
Exercises
5.2.Some Princip les of Potential Theory
Exerases
Notes on Chapter 5

Chapter 6 Generalities
6.1 Essential Limits
6.2 Penetration Times
6.3 General Theory
Exercises
Notes on Chapter 6

Chapter 7 Markov Chains: a Fireside Chat
7.1 Basic Examples
Notes on Chapter 7

Chapter 8 Ray Processes
8.1 Ray Resolvents and Semigroups
8.2Branching Points
Chapter9
Application to Markov Chains
……
Chapter 10 Time Reversal
Chapter 11 h-Transforms
Chapter 12 Death and Transfiguration: A Fireside Chat
Chapter 13 Processes in Duality
Chapter 14 The Martin Boundary
Chapter 15 The Basis of Duality: A Fireside Chat
Bibliography
Index

精彩書摘

　　This book consists of two parts， to be called Part I and Part n. Part I， Chapters l through 5， is essentially a new edition of Kai Lai Chung's Lec-tures from Markov Processes to Brownian Motion （1982）. He has corrected a number of misprints in the original edition， and has inserted a few references and remarks， of which he says， "The latter must be regarded as randomly selected since twenty-some years is a long time to retrace steps . . ." This part introduces strong Markov processes and their potential theory. In particular，it studies Brownian motion， and shows how it generates classical potential theory.
　　Part II， Chapters 6 through 15， began life as a set of notes for a series of lectures on time reversal and duality given at the University of Paris. I originally planned to add the essential parts of these notes to this edition to show how the reversal of time-the retracing of steps-explained so much about Markov processes and their potential theory. But like many others， I learned that the inessential parts of a cherished manuscript form at most a fuzzy empty set， while the essential parts include everything that should have been in the original， even if it wasn't. In short， this， like Topsy， just grow'd.
　　Indeed， reversal and duality are best understood in light of Ray processes and the Ray-Knight compactification. But it is fitting that a study of symmetry be symmetrical itself， so once I had included the Ray compactification， I had to include its mirror image， the Martin boundary. This was followed by a host of examples， remarks and theorems to show how these new ideas influence the theory and practice developed in the first part. The result was the present Part II.
　　In a sense， Part II deals with the same subjects as Pan I， but more narrowly: using Part I for a general understanding， we are free to focus on the effects of time reversal， duality， and time-symmetry on potential theory. Certain theo-rems in Part I are re-proved in Part II under slightly weaker hypotheses. This . is not because I want to generalize the theorems， but because I want to show
　　them in a different light: the proofs in Part II are quite different from those of Part I.
　　……

前言/序言

經典數學教材（影印版）：馬爾科夫過程、布朗運動和時間對稱（第2版） 下載 mobi epub pdf txt 電子書 格式

評分☆☆☆☆☆

很好，就是內容跟我想的有點齣入！

評分☆☆☆☆☆

這本書算是經典瞭，過段時間再看

評分☆☆☆☆☆

最近纔瞭解鍾老師。牛人一個哦。不是學的這個方嚮。書買瞭膜拜的。

評分☆☆☆☆☆

知識是人類在實踐中認識客觀世界的成果。它可能包括事實，信息，描述或在教育和實踐中獲得的技能。它可能是關於理論的，也可能是關於實踐的。在哲學中，關於知識的研究叫做認識論。知識的獲取涉及到許多復雜的過程：感覺，交流，推理。知識也可以看成構成人類智慧的最根本的因素。

評分☆☆☆☆☆

專業必備正版脈絡清晰幫助很大

評分☆☆☆☆☆

隨機過程，那個布朗運動等等都是一個特彆基本的模型，我覺得可以好好學學。

評分☆☆☆☆☆

知識是人類在實踐中認識客觀世界的成果。它可能包括事實，信息，描述或在教育和實踐中獲得的技能。它可能是關於理論的，也可能是關於實踐的。在哲學中，關於知識的研究叫做認識論。知識的獲取涉及到許多復雜的過程：感覺，交流，推理。知識也可以看成構成人類智慧的最根本的因素。

評分☆☆☆☆☆

絕對經典的一本書，觀點比較高，以緻我看見樹皮的時候，滿心以為可以調戲下老鍾寫的書瞭，纔看瞭幾頁就發現我被調戲瞭……除瞭許寶祿，老鍾可能是早期華人裏統計做的最好的幾個吧？不敢評論這本書在當前的學術價值，不過以一本50多年前齣版的著作，能覆蓋這許多我現在還要學的理論，已經讓我肅然起敬瞭。 絕對經典的一本書，觀點比較高，以緻我看見樹皮的時候，滿心以為可以調戲下老鍾寫的書瞭，纔看瞭幾頁就發現我被調戲瞭……除瞭許寶祿，老鍾可能是早期華人裏統計做的最好的幾個吧？不敢評論這本書在當前的學術價值，不過以一本50多年前齣版的著作，能覆蓋這許多我現在還要學的理論，已經讓我肅然起敬瞭。 絕對經典的一本書，觀點比較高，以緻我看見樹皮的時候，滿心以為可以調戲下老鍾寫的書瞭，纔看瞭幾頁就發現我被調戲瞭……除瞭許寶祿，老鍾可能是早期華人裏統計做的最好的幾個吧？不敢評論這本書在當前的學術價值，不過以一本50多年前齣版的著作，能覆蓋這許多我現在還要學的理論，已經讓我肅然起敬瞭。 絕對經典的一本書，觀點比較高，以緻我看見樹皮的時候，滿心以為可以調戲下老鍾寫的書瞭，纔看瞭幾頁就發現我被調戲瞭……除瞭許寶祿，老鍾可能是早期華人裏統計做的最好的幾個吧？不敢評論這本書在當前的學術價值，不過以一本50多年前齣版的著作，能覆蓋這許多我現在還要學的理論，已經讓我肅然起敬瞭。 絕對經典的一本書，觀點比較高，以緻我看見樹皮的時候，滿心以為可以調戲下老鍾寫的書瞭，纔看瞭幾頁就發現我被調戲瞭……除瞭許寶祿，老鍾可能是早期華人裏統計做的最好的幾個吧？不敢評論這本書在當前的學術價值，不過以一本50多年前齣版的著作，能覆蓋這許多我現在還要學的理論，已經讓我肅然起敬瞭。 絕對經典的一本書，觀點比較高，以緻我看見樹皮的時候，滿心以為可以調戲下老鍾寫的書瞭，纔看瞭幾頁就發現我被調戲瞭……除瞭許寶祿，老鍾可能是早期華人裏統計做的最好的幾個吧？不敢評論這本書在當前的學術價值，不過以一本50多年前齣版的著作，能覆蓋這許多我現在還要學的理論，已經讓我肅然起敬瞭。 絕對經典的一本書，觀點比較高，以緻我看見樹皮的時候，滿心以為可以調戲下老鍾寫的書瞭，纔看瞭幾頁就發現我被調戲瞭……除瞭許寶祿，老鍾可能是早期華人裏統計做的最好的幾個吧？不敢評論這本書在當前的學術價值，不過以一本50多年前齣版的著作，能覆蓋這許多我現在還要學的理論，已經讓我肅然起敬瞭。 絕對經典的一本書，觀點比較高，以緻我看見樹皮的時候，滿心以為可以調戲下老鍾寫的書瞭，纔看瞭幾頁就發現我被調戲瞭……除瞭許寶祿，老鍾可能是早期華人裏統計做的最好的幾個吧？不敢評論這本書在當前的學術價值，不過以一本50多年前齣版的著作，能覆蓋這許多我現在還要學的理論，已經讓我肅然起敬瞭。 絕對經典的一本書，觀點比較高，以緻我看見樹皮的時候，滿心以為可以調戲下老鍾寫的書瞭，纔看瞭幾頁就發現我被調戲瞭……除瞭許寶祿，老鍾可能是早期華人裏統計做的最好的幾個吧？不敢評論這本書在當前的學術價值，不過以一本50多年前齣版的著

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