The Phase Probability Density Function of a Random Walk in Two Dimensions.

Abstract

The problem of determining the phase probability density function of the resultant of an N-step non-isotropic random walk in two dimensions is examined. A formula is obtained for the joint probability density function of angle and radius of the resultant for arbitrary step angle probability density and for any number of steps. The theory of generalised functions concentrated on smooth manifolds is applied to the problem. Asymptotic solutions are obtained for the case where the phase probability density of each step is the same Gaussian function periodically wrapped on to the interval (-pi, -pi). In particular solutions are obtained for small phase variance for any number of steps and for large variance for both small and large numbers of steps. Throughout the paper a physical point of view is taken. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1981
Accession Number
ADA115935

Entities

People

  • B. C. Barber

Organizations

  • Royal Aircraft Establishment

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Agreements
  • Bessel Functions
  • Delta Functions
  • Fourier Series
  • Frequency
  • Gaussian Distributions
  • Generators
  • Integrals
  • Measurement
  • Monte Carlo Method
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Random Number Generators
  • Random Walk
  • Two Dimensional
  • Waves

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Statistical inference.