Geodesic
Asymptotics of the persistence exponent of integrated fractional Brownian motion and fractionally integrated Brownian motion
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 1, pp. 100-114 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the persistence probability for the integrated fractional Brownian motion and the fractionally integrated Brownian motion with parameter $H$, respectively. For the integrated fractional Brownian motion, we discuss a conjecture of Molchan and Khokhlov and determine the asymptotic behavior of the persistence exponent as $H\to 0$ and $H\to 1$, which is in accordance with the conjecture. For the fractionally integrated Brownian motion, also called the Riemann–Liouville process, we find the asymptotic behavior of the persistence exponent as $H\to 0$.
Keywords: Gaussian process, integrated fractional Brownian motion, one-sided exit problem, stationary process, zero crossing.
Mots-clés : persistence, Riemann–Liouville process 
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F. Aurzada; M. Kilian. Asymptotics of the persistence exponent of integrated fractional Brownian motion and fractionally integrated Brownian motion. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 1, pp. 100-114. http://geodesic.mathdoc.fr/item/TVP_2022_67_1_a5/

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