Abstract. We introduce a class of Gaussian processes with stationary increments which exhibit long-range dependence. The class includes fractional Brownian motion with Hurst parameter H > 1/2 as a typical example. We establish infinite and finite past prediction formulas for the processes in which the predictor coefficients are given explicitly in terms of the MA(∞) and AR(∞) coefficients. We a...

Consider a single server queue with unit service rate fed by an arrival process of the following form: sessions arrive at the times of a Poisson process of rate λ, with each session lasting for an independent integer time τ > 1, where P (τ = k) = pk with pk ∼ αk−(1+α)L(k), where 1 < α < 2 and L(·) is a slowly varying function. Each session brings in work at unit rate while it is active. Thus th...

Abstract We introduce a definition of long range dependence random processes and fields on an (unbounded) index space $T\subseteq \mathbb{R}^d$ in terms integrability the covariance indicators that function exceeds any given level. This is specifically designed to cover case functions with infinite variance. show value this new its connection limit theorems via some examples including subordina...

In this paper we examine monthly mean temperatures in 40 selected stations Siberia for the time period January 1937–December 2020 using long range dependence techniques. particular, use a fractionally integrated model that incorporates linear trend along with seasonal structure. Our results show first memory is present all significantly positive values differencing parameter, though, at same co...