Two Brownian particles with rank-based characteristics and skew-elastic collisions |
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Authors: | E Robert Fernholz Tomoyuki Ichiba Ioannis Karatzas |
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Institution: | 1. Intech Investment Management LLC, One Palmer Square, Suite 441, Princeton, NJ 08542, United States;2. Department of Statistics and Applied Probability, South Hall, University of California, Santa Barbara, CA 93106, United States;3. Department of Mathematics, Columbia University, MailCode 4438, New York, NY 10027, United States |
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Abstract: | We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coëfficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic collision, to perfect reflection of one particle on the other. These interactions are governed by the left- and right-local times at the origin for the distance between the two particles. We realize this diffusion in terms of appropriate, apparently novel systems of stochastic differential equations involving local times, which we show are well posed. Questions of pathwise uniqueness and strength are also discussed for these systems. |
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Keywords: | primary 60H10 60G44 secondary 60J55 60J60 |
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