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Probability Density of a Moving Particle

Author

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  • Alan Washburn

    (The Boeing Company, Seattle, Washington)

Abstract

This paper studies a particular random tour (continuous random walk): A particle moves in two dimensions at constant speed by choosing successive travel directions that are independent and uniformly distributed between 0 and 2π, with the lengths of the steps between direction changes being independent, exponentially distributed, random variables. An analytic expression for the probability density of the particle's position after a time t is derived, and an application is made to a military situation where the “particle” is a target trying to escape being destroyed by an unseen enemy. The bulk of the paper is devoted to deriving the density function.

Suggested Citation

  • Alan Washburn, 1969. "Probability Density of a Moving Particle," Operations Research, INFORMS, vol. 17(5), pages 861-871, October.
  • Handle: RePEc:inm:oropre:v:17:y:1969:i:5:p:861-871
    DOI: 10.1287/opre.17.5.861
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