  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.

Probability