Let f:R?R be a stationary centered Gaussian process. For any R>0, let ?R denote the counting measure of {x?R?f(Rx)=0}. Under suitable assumptions on regularity f and decay its correlation function at infinity, we derive asymptotics as R?+? central moments linear statistics ?R. In particular, an order Rp 2 for p-th moment number zeros in [0,R]. As application, prove functional Law Large Numbers ...

In the present paper we study asymptotic behavior of auto-covariance function for Ornstein–Uhlenbeck (OU) processes driven by Gaussian noises with stationary and non-stationary increments Hermite OU processes. Our results are generalizations corresponding Cheridito et al. Kaarakka Salminen.