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Standard and fractional reflected OU processes in connection to square roots of CIR processes

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FD2W03 - Optimal control and fractional dynamics

We establish a new connection between Cox-Ingersoll-Ross (CIR)and reflected Ornstein-Uhlenbeck (ROU) models driven by either a standard Wienerprocess or a fractional Brownian motion with H > 1/2. We prove that, with probability1, the square root of the CIR process converges uniformly on compacts to the ROUprocess as the mean reversion parameter tends to either sigma^2/4 (in the standard case)or to 0 (in the fractional case). This also allows to obtain a new representation of thereflection function of the ROU as the limit of integral functionals of the CIR processes.The results   are illustrated by simulations.

This talk is part of the Isaac Newton Institute Seminar Series series.

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