2017
Jun
20

# Dynamics seminar:Naomi Feldheim (Stanford): Persistence of Gaussian Stationary Processes

2:00pm to 3:00pm

Consider a real Gaussian stationary process, either on Z or on R. That is,

a stochastic process, invariant under translations, whose finite marginals

are centered multi-variate Gaussians. The persistence of such a process on

[0,N] is the probability that it remains positive throughout this interval.

The relation between the decay of the persistence as N tends to infinity

and the covariance function of the process has been investigated since the

1950s with motivations stemming from probability, engineering and

a stochastic process, invariant under translations, whose finite marginals

are centered multi-variate Gaussians. The persistence of such a process on

[0,N] is the probability that it remains positive throughout this interval.

The relation between the decay of the persistence as N tends to infinity

and the covariance function of the process has been investigated since the

1950s with motivations stemming from probability, engineering and