Persistence probabilities of a smooth self-similar anomalous diffusion process
| Autor: | Aurzada, Frank, Mittenbühler, Pascal |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | We consider the persistence probability of a certain fractional Gaussian process $M^H$ that appears in the Mandelbrot-van Ness representation of fractional Brownian motion. This process is self-similar and smooth. We show that the persistence exponent of $M^H$ exists and is continuous in the Hurst parameter $H$. Further, the asymptotic behaviour of the persistence exponent for $H\downarrow0$ and $H\uparrow1$, respectively, is studied. Finally, for $H\to 1/2$, the suitably renormalized process converges to a non-trivial limit with non-vanishing persistence exponent, contrary to the fact that $M^{1/2}$ vanishes. Comment: 25 pages |
| Databáze: | arXiv |
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