Principles of random walk随机游动的原则
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作者： Frank Spitzer著
出 版 社：
出版时间： 2001-3-1字数：版次： 1页数： 408印刷时间： 2001/03/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387951546包装： 平装内容简介
This book is devoted exclusively to a very special class of random processes, namely to random walk on the lattice points of ordinary Euclidean space. The author considered this high degree of specialization worthwhile, because of the theory of such random walks is far more complete than that of any larger class of Markov chains. The book will present no technical difficulties to the readers with some solid experience in analysis in two or three of the following areas: probability theory, real variables and measure, analytic functions, Fourier analysis, differential and integral operators. There are almost 100 pages of examples and problems.
目录
CHAPTER. Ⅰ The Classification of Random Walk
1 Introduction
2 Periodicity and recurrence behavior
3 Some measure theory
4 The range of a random walk
5 The strong ratio theorem
CHAPTER. Ⅱ Harmonic Analysis
6 CHAPTERaracteristic functions and moments
7 Periodicity
8 Recurrence criteria and examples
9 The renewal theorem
CHAPTER. Ⅲ Two-Dimensional Recurrent Random Walk
10 Generalities
11 The hitting probabilities of a finite set
12 The potential kernel A(x,y)
13 Some potential theory
14 The Green function of a finite set
15 Simple random walk in the plane
16 The time dependent behavior
CHAPTER. Ⅳ Random Walk on a Half-Line
17 The hitting probability of the right half-line
18 Random walk with finite mean
19 The Green function and the gambler's ruin problem
20 Fluctuations and the arc-sine law
CHAPTER. Ⅴ Random Walk on a Interval
21 Simple random walk
22 The absorption problem with mean zero, finite variance
23 The Green function for the absorption problem
CHAPTER. Ⅵ Transient Random Walk
24 The Green function G(x,y)
25 Hitting probabilities
26 Random walk in three-space with mean zero and finite second moments
27 Applications to analysis
CHAPTER. Ⅶ Recurrent Random Walk
28 The existence of the one-dimensional potential kernel
29 The asymptotic behavior of the potential kernel
30 Hitting probabilities and the Green function
31 The uniqueness of the recurrent potential kernel
32 The hitting time of a single point
Bibliography
Supplementary Bibliography
Index
