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Strong Solutions to a Beta-Wishart Particle System

Author

Listed:
  • Benjamin Jourdain

    (INRIA)

  • Ezéchiel Kahn

    (INRIA)

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.

Suggested Citation

  • Benjamin Jourdain & Ezéchiel Kahn, 2022. "Strong Solutions to a Beta-Wishart Particle System," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1574-1613, September.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:3:d:10.1007_s10959-021-01109-1
    DOI: 10.1007/s10959-021-01109-1
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    References listed on IDEAS

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    1. Andraus, Sergio & Voit, Michael, 2019. "Limit theorems for multivariate Bessel processes in the freezing regime," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4771-4790.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. Bru, Marie-France, 1989. "Diffusions of perturbed principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 127-136, April.
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