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

mathematical physics. Nonetheless, until recently, good estimates were

known only for particular cases, or when the covariance kernel of the

process is either non-negative or summable.

In the talk we discuss a new spectral point of view on persistence which

greatly simplifies its analysis. This is then used to analyze the

qualitative behavior of the persistence probability in a very general

setting.

Based on joint work with Ohad Feldheim and Shahaf Nitzan.

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

mathematical physics. Nonetheless, until recently, good estimates were

known only for particular cases, or when the covariance kernel of the

process is either non-negative or summable.

In the talk we discuss a new spectral point of view on persistence which

greatly simplifies its analysis. This is then used to analyze the

qualitative behavior of the persistence probability in a very general

setting.

Based on joint work with Ohad Feldheim and Shahaf Nitzan.

## Date:

Tue, 20/06/2017 - 14:00 to 15:00