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arXiv · 2003.08699

Strong solutions to a beta-Wishart particle system

Benjamin Jourdain·Ezéchiel Kahn
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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 SDE for this multiple collision not to occur in finite time.

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Benjamin Jourdain, Ezéchiel Kahn. 2020-03-19. Strong solutions to a beta-Wishart particle system. https://arxiv.org/abs/2003.08699

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