Random walk in random and non-random environments随机和非随机环境下的随机移动
点此进入淘宝搜索页搜索分類: 图书,进口原版书,科学与技术 Science & Techology ,
作者： Pal Revesz著
出 版 社：
出版时间： 2005-8-30字数：版次： 1页数： 380印刷时间： 2005/08/30开本： 16开印次： 1纸张： 胶版纸I S B N ： 9789812563613包装： 精装内容简介
The simplest mathematical model of the Brownian motion of physics is the simple ,symmetric random walk ,this book collects and compares current results–walk ,the modern problems of the limit the orems of probability the ,reader is familiarized with limit theorems(especially strong ones )without the burden of technical tools and difficulties .an easy way of considering the wiener process is also given ,the rough the study of the random walk.
目录
Contents
Preface to the First Edition
Preface to the Second E；dition
Introduction
Ⅰ.SIMPLE SYMMETRIC RANDOM WALK IN Zl
Notations and abbreviations
1Introduction of Part Ⅰ
1.1 Random walk
1.2 Dyadic expansions
1.3 Rademacher functions
1.4 Coin tossin9
1.5 The language of the probabilist0
2 Distributions
2.1 Exact distributions
2.2 Limit distributions
3 Recurrence and the Zero-One Law
3.1 Recurrence
3.2 The zero-one Law0
4 From the Strong Law of Large Numbers to the Law of Iterated Logarithm
4.1 Borel-Cantelli lemma and Markov inequality
4.2 The strong law of large numbers
4.3 Between the strong law of large numbers and the law of iterated logarithm0
4.4 The LIL of Khinchine
5 Lgvy Classes
5.1 Definitions
5.2 EFKP LIL
5.3 The laws of Chung and Hirsch0
5.4 When will Sn be very large
5.5 A theorem of Csaki
6 Wiener Process and Invariance Principle
6.1 Four lemmas
6.2 Joining of independent random walks
6.3 Definition of the Wiener process
6.4 Invariance Principle
7 Increments
7.1 Long headruns
7.2 The increments of a Wiener process
7.3 The increments of SN
8 Strassen Type Theorems
8.1 The theorem of Strassen
8.2 Strassen theorems for increments
8.3 The rate of convergence in Strassen’S theorems
8.4 A theorem of Wichura
9 Distribution of the Local Time
9.1 Exact distributions
9.2 Limit distributions
9.3 Definition and distribution of the local time of a Wiener process
10 Local Time and Invariance Principle
10.1 An invariance principle
10.2 A theorem of L6vy
11 strong theorems of the local time
12 excursions
13 frequently and rarely visited sites
14 an embedding theorem
15 a few further results
16 summary of part Ⅰ
Ⅱ.SIMPLE SYMMETRIC RANDOM WALK IN
17 the recurrence theorem
18 wiener process and invariance principle
19 the law of iterated logarithm
20 local time
21 the range
22 heavy points and heavy balls
23 Grossing and self-crossing
24 large couered balls
25 long excur sions
26 speedof escape
27 A fEW Further problems
Ⅲ.RANDOM WALK IN RANDOM ENVIRONMENT NOTATIONS
28 INthe first six days
29 After the sixthe day
30 after the sixthe day
31 what can a phyaicist say about the local time
32 on the favourite value of the RWIRE
33 A Few further problems
References
Autheor indwx
Subject index