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

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 $H\to 0$.

Minor corrections

References in corpus (2)

• Random walks and branching processes in correlated Gaussian environment
• Persistence probabilities of weighted sums of stationary Gaussian sequences

Cited by in corpus (2)

• Stochastic kinetics under combined action of two noise sources
• Persistence probabilities of mixed FBM and other mixed processes