A Problem on Random Walk

Abstract

From an urn containing an equal number of each of I kinds of balls, random drawings are made. After each drawing the ball is returned to the urn, so that each drawing is independent of every other. If the drawings are repeated indefinitely, what is the probability that after some drawing in the sequence an equal number of each of the I kinds of balls will have been drawn? This problem can be interpreted as a random walk in a network of "streets" in (I -1)-dimensional space. The drawing of a ball of a given kind is represented by the walker's moving a fixed distance in a given direction. Equalization is represented by a return to the origin.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1951
Accession Number
AD1028688

Entities

People

  • R. S. Lehman

Organizations

  • Stanford University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • California
  • Equalization
  • Governments
  • Inequalities
  • Mathematics
  • New York
  • Polynomials
  • Probability
  • Random Walk
  • Sequences
  • Statistics
  • Three Dimensional
  • United States
  • United States Government
  • Universities

Readers

  • Graph Algorithms and Convex Optimization.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space
  • Space - Space Objects