A Mean-Reverting SDE on Correlation matrices
Résumé
We introduce a mean-reverting SDE whose solution is naturally defined on the space of correlation matrices. This SDE can be seen as an extension of the well-known Wright-Fisher diffusion. We provide conditions that ensure weak and strong uniqueness of the SDE, and describe its ergodic limit. We also shed light on a useful connection with Wishart processes that makes understand how we get the full SDE. Last, we focus on the simulation of this diffusion and present discretization schemes that achieve a second-order weak convergence.
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