機率和隨機

《機率和隨機》是2015年世界圖書出版公司出版的圖書，作者是Erhan Çınlar。

基本介紹

• 中文名：機率和隨機
• 作者：Erhan Çınlar
• ISBN：9787510086298
• 頁數：557
• 出版社：世界圖書出版公司
• 出版時間：2015-1-1
• 裝幀：平裝

內容簡介

《機率和隨機》是一部兼顧理論和套用的，講述機率和隨機研究生教材。本書的風格仍然是這個系列的延續，注重隨機過程的理論，但卻非一味強調理論和抽象，也兼顧套用。書的前四章是有關機率論、度量和積分、機率空間、條件期望和經典極限定理；接下來的章節是有關鞅、泊松隨機測度、levy過程、布朗運動和馬爾科夫過程。重點強調了泊松隨機測度，及其在調節布朗運動衝程和Levy躍遷和馬爾科夫過程中的扮演的重要角色。每章末都有大量的例子和練習。

目錄

Preface

Frequently Used Notation

Ⅰ Measure and Integration

1 Measurable Spaces

2 Measurable Functions

3 Measures

4 Integration

5 Transforms and Indefinite Integrals

6 Kernels and Product Spaces

Ⅱ Probability Spaces

1 Probability Spaces and Random Variables

2 Expectations

3 LP—spaces and Uniform Integrability

4 Information and Determinability

5 Independence

Ⅲ Convergence

1 Convergence of Real Sequences

2 Almost Sure Convergence

3 Convergence in Probability

4 Convergencein Lp

5 Weak Convergence

6 Laws ofLarge Numbers

7 Convergence ofSeries

8 CentraILimits

Ⅳ Conditioning

1 Conditional Expectations

2 Conditional Probabilities and Distributions

3 Conditionallndependence

4 Construction of Probability Spaces

5 Special Constructions

Ⅴ Martingales and Stochastics

1 Filtrations and Stopping Times

2 Martingales

3 Martingale Transformations and Maxima

4 Martingale Convergence

5 Martingales in Continuous Time

6 Martingale Characterizations for Wiener and Poisson

7 Standard Filtrations and Modifications of Martingales

Ⅵ Poisson Random Measures

1 Random Measures

2 Poisson Random Measures

3 Transformations

4 Additive Random Measures and Levy Processes

5 Poisson Processes

6 Poisson Integrals and Self—exciting Processes

Ⅶ Levy Processes

1 Introduction

2 Stable Processes

3 Levy Processes on Standard Settings

4 Characterizations for Wiener and Poisson

5 Ito—Levy Decomposition

6 Subordination

7 Increasing Levy Processes

Ⅷ Brownian Motion

1 Introduction

2 Hitting Times and Recurrence Times

3 Hitting Times and Running Maximum

4 Wiener and its Maximum

5 Zeros，LocaITimes

6 Excursions

7 Path Properties

8 Existence

Ⅸ Markov Processes

1 Markov Property

2 Ito Diffusions

3 Jump—Diffusions

4 Markov Systems

5 Hunt Processes

6 Potentials and Excessive Functions

7 Appendix：Stochastic Integration

Notes and Comments

Bibliography

Index