Principles of Random Walk / by Frank Spitzer.

Format:

Book

Author/Creator:

Spitzer, Frank, 1926- author.

Contributor:

SpringerLink (Online service)

Series:

Graduate texts in mathematics 2197-5612 ; 34.

Graduate Texts in Mathematics, 2197-5612 ; 34

Language:

English

Subjects (All):

Probabilities.

Probability Theory and Stochastic Processes.

Local Subjects:

Probability Theory and Stochastic Processes.

Physical Description:

1 online resource (XIII, 408 pages).

Edition:

Second edition 1964.

Contained In:

Springer Nature eBook

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1964.

System Details:

text file PDF

Summary:

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].

Contents:

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.

Other Format:

Printed edition:

ISBN:

9781475742299

Access Restriction:

Restricted for use by site license.