| 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 |
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