Principles of random walk
By: Frank Spitzer.
Edition: 2nd ed.
Series: Graduate texts in mathematics ;; 34
Publisher: Springer
Published: 2001
Place of publication: New York
Language: eng
Number of pages: 408
Subjects: Random walks (Mathematics)
Description: "This book is devoted to the study of random walk on the lattice points of ordinary Euclidean space. The theory of random walks, a central part of the theory of Markov chains, is connected with methods from harmonic analysis on the one hand and from potential theory on the other. Prerequisites for the book are some knowledge of two or three of the following areas: probability theory, real variables and measure, analytic functions, Fourier analysis, differential, and integral operators.

More than 100 pages of examples and problems illustrate and clarify the presentation."--BOOK JACKET.
Notes: Includes bibliographical references (p. 403-408) and index.
Table of contents: title: Machine generated contents note: CHAPTER I. THE CLASSIFICATION OF RANDOM WALK; title: 1. Introduction; title: 2. Periodicity and recurrence behavior; title: 3. Some measure theory; title: 4. The range of a random walk; title: 5. The strong ratio theorem; title: Problems CHAPTER II. HARMONIC ANALYSIS; title: 6. Characteristic functions and moments; title: 7. Periodicity; title: 8. Recurrence criteria and examples; title: 9. The renewal theorem; title: Problems CHAPTER III. Two-DIMENSIONAL RECURRENT RANDOM WALK; title: 10. Generalities; title: 11. The hitting probabilities of a finite set; title: 12. The potential kernel A(x,y); title: 13. Some potential theory; title: 14. The Green function of a finite set; title: 15. Simple random walk in the plane; title: 16. The time dependent behavior; title: Problems CHAPTER IV. RANDOM WALK ON A HALF-LINE; title: 17. The hitting probability of the right half-line; title: 18. Random walk with finite mean; title: 19. The Green function and the gambler's ruin problem; title: 20. Fluctuations and the arc-sine law; title: Problems; title: CHAPTER V. RANDOM WALK ON A INTERVAL; title: 21. Simple random walk; title: 22. The absorption problem with mean zero, finite variance; title: 23. The Green function for the absorption problem; title: Problems CHAPTER VI. TRANSIENT RANDOM WALK; title: 24. The Green function G(x,y); title: 25. Hitting probabilities; title: 26. Random walk in three-space with mean zero and finite; title: second moments; title: 27. Applications to analysis; title: Problems CHAPTER VII. RECURRENT RANDOM WALK; title: 28. The existence of the one-dimensional potential kernel; title: 29. The asymptotic behavior of the potential kernel; title: 30. Hitting probabilities and the Green function; title: 31. The uniqueness of the recurrent potential kernel; title: 32. The hitting time of a single point; title: Problems; title: BIBLIOGRAPHY SUPPLEMENTARY BIBLIOGRAPHY INDEX.