Student Probability Seminar

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On the persistence probability of Gaussian stationary processes

Speaker: Santi Aranguri, Courant (NYU)

Location: Warren Weaver Hall 517

Date: Monday, October 17, 2022, 1 p.m.

Synopsis:

We study the "persistence probability" of a Gaussian stationary process, which is the probability that the process stays above a constant value L for a fixed interval of time. We will characterize this probability asymptotically in terms of the Fourier transform of the covariance of the process, with a particular interest in L = 0. We then prove a "continuity in the exponent" result, which means that the limit as the length of the interval goes to infinity of the normalized persistence probability depends continuously on L.