TY - JOUR
T1 - Strong Solutions to a Beta-Wishart Particle System
AU - Jourdain, Benjamin
AU - Kahn, Ezéchiel
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/9/1
Y1 - 2022/9/1
N2 - 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.
AB - 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.
KW - Diffusions with gradient drift
KW - Random matrices
KW - Singular interaction
KW - Stochastic differential equations
UR - https://www.scopus.com/pages/publications/85109803809
U2 - 10.1007/s10959-021-01109-1
DO - 10.1007/s10959-021-01109-1
M3 - Article
AN - SCOPUS:85109803809
SN - 0894-9840
VL - 35
SP - 1574
EP - 1613
JO - Journal of Theoretical Probability
JF - Journal of Theoretical Probability
IS - 3
ER -