Random walks on compact semigroups
Authors:
A. Mukherjea, T. C. Sun and N. A. Tserpes
Journal:
Proc. Amer. Math. Soc. 39 (1973), 599-605
MSC:
Primary 60J15; Secondary 60B15
DOI:
https://doi.org/10.1090/S0002-9939-1973-0317420-X
MathSciNet review:
0317420
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a regular Borel probability measure with support
on a compact semigroup
. Let
be a sequence of independent random variables on some probability space
with values in
, having identical distribution
. The random walk
is studied in this paper. Let
be the closed semigroup generated by
. An element
in
is called recurrent iff
for every open set
containing
. This paper characterizes the recurrence of an element
in terms of divergence of the series
for every open set
containing
. It also shows that the set of recurrent states of
is precisely the kernel of
.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1973-0317420-X
Keywords:
Topological semigroup,
kernel of a semigroup,
recurrent random walks
Article copyright:
© Copyright 1973
American Mathematical Society