Strong Solutions to a Beta-Wishart Particle System

Benjamin Jourdain () and Ezéchiel Kahn ()
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Benjamin Jourdain: INRIA
Ezéchiel Kahn: INRIA

Journal of Theoretical Probability, 2022, vol. 35, issue 3, 1574-1613

Abstract: Abstract The purpose of this paper is to study the existence and uniqueness of solutions to a stochastic differential equation (SDE) coming from the eigenvalues of Wishart processes. The coordinates are non-negative, evolve as Cox–Ingersoll–Ross (CIR) processes and repulse each other according to a Coulombian like interaction force. We show the existence of strong and pathwise unique solutions to the system until the first multiple collision and give a necessary and sufficient condition on the parameters of the SDEs for this multiple collision not to occur in finite time.

Keywords: Stochastic differential equations; Diffusions with gradient drift; Singular interaction; Random matrices; 60H10; 60J60; 60B20; 60G17; 60J70 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01109-1

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