Standard and fractional reflected OU processes in connection to square roots of CIR processes
Duration: 45 mins 9 secs
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| Description: |
Yuliya Mishura (Taras Shevchenko National University of Kyiv)
19/04/2022 Programme: FD2W03 SemId: 35389 |
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| Created: | 2022-05-02 02:03 |
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| Collection: | Fractional differential equations |
| Publisher: | Yuliya Mishura |
| Copyright: | Isaac Newton Institute |
| Language: | eng (English) |
| Abstract: | We establish a new connection between Cox-Ingersoll-Ross (CIR)
and reflected Ornstein-Uhlenbeck (ROU) models driven by either a standard Wiener process or a fractional Brownian motion with H > 1/2. We prove that, with probability 1, the square root of the CIR process converges uniformly on compacts to the ROU process 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 the reflection function of the ROU as the limit of integral functionals of the CIR processes. The results are illustrated by simulations. |
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