Two Brownian particles with rank-based characteristics and skew-elastic collisions

E. Robert Fernholz, Tomoyuki Ichiba and Ioannis Karatzas

Stochastic Processes and their Applications, 2013, vol. 123, issue 8, 2999-3026

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.

Keywords: Diffusion; Local time; Skew Brownian motion; Time reversal; Brownian motion reflected on Brownian motion (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (9)

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DOI: 10.1016/j.spa.2013.03.019

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