Random Walk on a Half-Line
Part of the Graduate Texts in Mathematics book series (GTM, volume 34)
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 a ≤ x < ∞ or ∞ − ∞ < x ≤ a, where a is a point (integer) in R. When B ⊂ R is such a set it goes without saying that one can define the functions
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.
KeywordsRandom 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.
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© Frank Spitzer 1964