Behavior of Convolution Sequences of a Family of Probability Measures on The Interval (0, Infinity),

Abstract

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 n)(O) 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 interval(0, infinity) which shows that Rosenblatt's 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.

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1973
Accession Number
ADA001241

Entities

People

  • A. Mukherhea
  • E. B. Saff

Organizations

  • University of South Florida

Tags

DTIC Thesaurus Topics

  • Convolution
  • Exponential Functions
  • Intervals
  • Mathematics
  • Polynomials
  • Probability
  • Random Walk
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Graph Algorithms and Convex Optimization.
  • Statistical inference.