Spitzer Principles of Random Walk

2. Auflage 1964
ISBN: 978-1-4757-4229-9
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 34, 408 Seiten, eBook

Reihe: Graduate Texts in Mathematics

In this edition a large number of errors have been corrected, an occasional proof has been streamlined, and a number of references are made to recent pro gress. These references are to a supplementary bibliography, whose items are referred to as [S1] through [S26]. A thorough revision was not attempted. The development of the subject in the last decade would have required a treatment in a much more general con text. It is true that a number of interesting questions remain open in the concrete setting of random walk on the integers. (See [S 19] for a recent survey). On the other hand, much of the material of this book (foundations, fluctuation theory, renewal theorems) is now available in standard texts, e.g. Feller [S9], Breiman [S1], Chung [S4] in the more general setting of random walk on the real line. But the major new development since the first edition occurred in 1969, when D. Ornstein [S22] and C. J. Stone [S26] succeeded in extending the recurrent potential theory in· Chapters II and VII from the integers to the reals. By now there is an extensive and nearly complete potential theory of recurrent random walk on locally compact groups, Abelian ( [S20], [S25]) as well as non Abelian ( [S17], [S2] ). Finally, for the non-specialist there exists now an unsurpassed brief introduction to probabilistic potential theory, in the context of simple random walk and Brownian motion, by Dynkin and Yushkevich [S8].

Zielgruppe

Graduate

Autoren/Hrsg.

Spitzer, Frank

Inhaltsverzeichnis

I. The Classification of Random Walk.- II. Harmonic Analysis.- III. Two-Dimensional Recurrent Random Walk.- IV. Random Walk on a Half-Line.- V. Random Walk on a Interval.- VI. Transient Random Walk.- VII. Recurrent Random Walk.- Supplementary Bibliography.