Persistence probabilities of two-sided (integrated) sums of correlated stationary Gaussian sequences

Abstract

We study the persistence probability for some two-sided discrete-time Gaussian sequences that are discrete-time analogs of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the corresponding ones in continuous-time in [Molchan, Commun. Math. Phys., 1999] and [Molchen, J. Stat. Phys., 2017] to a wide class of discrete-time processes.

20 pages

References in corpus (2)

• Anomalous fluctuations of currents in Sinai-type random chains with strongly correlated disorder
• The inviscid Burgers equation with fractional Brownian initial data: the dimension of regular Lagrangian points

Cited by in corpus (2)

• Penalizing fractional Brownian motion for being negative
• Persistence probabilities of mixed FBM and other mixed processes