Behavior of Convolution Sequences of a Family of Probability Measures on The Interval (0, Infinity),
UNIVERSITY OF SOUTH FLORIDA TAMPA DEPT OF MATHEMATICS
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In this paper, the authors, consider a result due to M. Rosenblatt which is frequently useful in the theory of random walks. His result states that if mu is a regular probability measure on a compact semigroup S which is generated by the support of mu, then given any open set O containing an ideal of S, mu sup nO converges to 1 as n nears infinity. The essential contribution of this paper is an example of an interesting family of probability measures on the interval0, infinity which shows that Rosenblatts theorem cannot be extended to a general locally compact semigroup. Of further significance in this paper is the indicated relationship between the Central Limit Theorem of probability theory on the one hand and polynomial approximation of the exponential function on the other.
- Statistics and Probability