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Persistence probabilities of two-sided (integrated) sums of correlated stationary Gaussian sequences (1710.05777v1)
Published 16 Oct 2017 in math.PR
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.