Persistence Probabilities of Two-Sided (Integrated) Sums of Correlated Stationary Gaussian Sequences

We study the persistence probability for some two-sided, discrete-time Gaussian sequences that are discrete-time analogues of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the corresponding ones in continuous time in Molchan (Commun Math Phys 205(1):97–111, 1999) and Molchan (J Stat Phys 167(6):1546–1554, 2017) to a wide class of discrete-time processes.