Random Walk on a Half-Line

  • Frank Spitzer
Part of the Graduate Texts in Mathematics book series (GTM, volume 34)

Abstract

For one-dimensional random walk there is an extensive theory concerning a very special class of infinite sets. These sets are half-lines, i.e., semi-infinite intervals of the form ax < ∞ or ∞ − ∞ < xa, where a is a point (integer) in R. When BR is such a set it goes without saying that one can define the functions
$${Q_n}(x,y),{H_B}(x,y),{g_B}(x,y),x,yinR,$$
just as in section 10, Chapter III. Of course the identities discovered there remain valid—their proof having required no assumptions whatever concerning the dimension of R, the periodicity or recurrence of the random walk, or the cardinality of the set B.

Keywords

Random Walk Fourier Series Green Function Simple Random Walk Outer Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Frank Spitzer 1964

Authors and Affiliations

  • Frank Spitzer
    • 1
  1. 1.Department of MathematicsCornell UniversityIthacaUSA

Personalised recommendations