Event № 1355

 The $N$ persistence probability of a stationary process is the pr obability that it is positive on a time interval  of length $N$. On the int=obability that it is positive on a time interval  of length $N$. On the integers, the independent sequence has persistence  probability $2^{-N}$. It is therefore natural to conjecture that in general, given sufficient independence, the persistence probability of stationary Gaussian  processes will decay exponentially.

In the talk we formulate in spectral language simple broad sufficient conditions for upper and lower exponential bounds on the persistence probability. The results hold also for Gaussian processes on the real line, and generalize bounds given by Newell and Rosenblatt in the 1960's, and by Antezana, Buckley, Marzo and Olsen in 2012.

Joint work with Ohad Feldheim.