We establish sufficient conditions on durations that arestationary with finite variance and memory parameter $d \in[0,1/2)$ to ensure that the corresponding counting process $N(t)$satisfies $Var N(t) \sim C t^{2d+1}$ ($Cgt;0$) as $t\rightarrow \infty$, with the same memory parameter $d...

For long-memory time series, we show that the Toeplitz system sect;n(f)x = b can be solved inO(n log5=2 n) operations using a well-known version of the preconditioned conjugate gradient method, where sect;n(f) is the npound;n covariance matrix, f is the spectral density and b is a known vector....