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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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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DOI: https://doi.org/10.1007/s004400100160
Keywords
- Brownian Motion
- Local Time
- Probability Space
- Initial Velocity
- Velocity Versus