INVESTIGATIONS ON FLUCTUATIONS OF SUMS OF RANDOM VARIABLES

Abstract

We have investigated the fluctuations of sums of random variables X1, X2,. We have generalized previous results on the random variables Hn connected with this sequence, obtained new results on the validity of the Arc-sine Law for independent not identically distributed random variables, obtained a generalization of Spitzer's identity, and obtained a generalization of the equivalence principle. Furthermore Toeplitz matrices of Laurent polynomials have been studied. For the growth of the maximal order statistics of a sequence of independent, identically distributed random variables a ''Law of the iteratedlogarithm'' has been obtained.

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Document Details

Document Type
Technical Report
Publication Date
Jul 15, 1963
Accession Number
AD0416361

Entities

People

  • E. S. Andersen

Organizations

  • Aarhus University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Contracts
  • Distribution Functions
  • Functional Analysis
  • Integral Equations
  • Law
  • Markov Chains
  • New York
  • Numbers
  • Order Statistics
  • Polynomials
  • Probability
  • Random Variables
  • Real Numbers
  • Sequences
  • Stochastic Processes
  • Three Dimensional
  • United States

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Mathematical Modeling and Probability Theory.