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Convergence of Isotropic Scattering Transport Process to Brownian Motion

Published online by Cambridge University Press:  22 January 2016

Shinzo Watanabe  and
Toitsu Watanabe
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Let us consider transporting particle in the n-dimensional Euclidian space Rn. It is assumed that a particle originating at a point x∈Rn moves in a straight line with constant speed c and continues to move until it suffers a collision. The probability that the particle has a collision between t and t + Δ is kΔ + o(Δ), where k is constant. When a particle has a collision, say at y in Rn, it moves afresh from y with an isotropic choice of direction independent of past history.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 40 , December 1970 , pp. 161 - 171
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

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