Probability Density of a Moving Particle

Alan Washburn
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Alan Washburn: The Boeing Company, Seattle, Washington

Operations Research, 1969, vol. 17, issue 5, 861-871

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.

Date: 1969
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:17:y:1969:i:5:p:861-871

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