The Bethe ansatz for sticky Brownian motions

Dom Brockington and Jon Warren

Stochastic Processes and their Applications, 2023, vol. 162, issue C, 1-48

Abstract: We consider a multi-dimensional diffusion whose coordinates behave as one-dimensional Brownian motions, evolving independently when apart, but with a sticky interaction when they coincide. We derive the Kolmogorov backwards equation and show that for a specific choice of interaction it can be solved exactly with the Bethe ansatz. The diffusion in Rn can be viewed as the n-point motions of a stochastic flow of kernels. We use our formulae to study the flow of kernels and show that atoms in the flow are asymptotically exponentially distributed in size at large times.

Keywords: Bethe ansatz; Sticky Brownian motions; Stochastic flows (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2023.04.015

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