Principles of random walk / Frank Spitzer.

Machine generated contents note: 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 -- Problems CHAPTER II. HARMONIC ANALYSIS -- 6. Characteristic functions and moments -- 7. Periodicity -- 8. Recurrence criteria and examples -- 9. The renewal theorem -- Problems 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 -- Problems 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 -- Problems -- 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 -- Problems 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 -- Problems 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 -- Problems -- BIBLIOGRAPHY SUPPLEMENTARY BIBLIOGRAPHY INDEX.