Asymptotics of the persistence exponent of integrated fractional Brownian motion and fractionally integrated Brownian motion

Frank Aurzada; Martin Kilian

doi:10.1137/s0040585x97t990769

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arXiv · 2007.01254

Asymptotics of the persistence exponent of integrated fractional Brownian motion and fractionally integrated Brownian motion

Frank Aurzada·Martin Kilian

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Abstract

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 Riemann-Liouville process, we find the asymptotic behavior of the persistence exponent as $H\to 0$.

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Frank Aurzada, Martin Kilian. 2020-07-02. Asymptotics of the persistence exponent of integrated fractional Brownian motion and fractionally integrated Brownian motion. https://doi.org/10.1137/s0040585x97t990769

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