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On the path of an inert object impinged on one side by a Brownian particle
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  • Published: December 2001

On the path of an inert object impinged on one side by a Brownian particle

  • Frank B. Knight1 

Probability Theory and Related Fields volume 121, pages 577–598 (2001)Cite this article

  • 148 Accesses

  • 15 Citations

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Abstract.

A Brownian particle on R impinges at t = 0 on an inertial mass which is free to move but cannot be passed. We assume that for all t≥ 0 the total transfer of momentum by time t is a constant K times the local time that the two objects are in contact by time t. It is proved that, for each K > 0 and initial velocity V(0) of the inertial mass, there is, on the natural filtered probability space of a Brownian motion, a unique (in law) process describing the path of such a mass. If V(t) denotes its velocity, the law of V (-1)(t) is obtained explicitly for V(0) = 0, and its properties are examined.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA. e-mail: davison@math.uiuc.edu, , , , , , US

    Frank B. Knight

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  1. Frank B. Knight
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Received: 22 August 2000 / Revised version: 31 January 2001 / Published online: 9 October 2001

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Knight, F. On the path of an inert object impinged on one side by a Brownian particle. Probab Theory Relat Fields 121, 577–598 (2001). https://doi.org/10.1007/s004400100160

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  • Issue Date: December 2001

  • DOI: https://doi.org/10.1007/s004400100160

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Keywords

  • Brownian Motion
  • Local Time
  • Probability Space
  • Initial Velocity
  • Velocity Versus
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