We obtain limit theorems for a class of nonlinear discrete-time processes X(n) called the kth order Volterra processes of order k. These are moving average kth order polynomial forms: X(n)=∑0i1,…,ik∞a(i1,…,ik)ϵn−i1…ϵn−ik, where {ϵi} is i.i.d. with Eϵi=0, Eϵi2=1, where a(⋅)...

In Puplinskaitė and Surgailis (2014) we introduced the notion of scaling transition for stationary random fields X on Z2 in terms of partial sums limits, or scaling limits, of X over rectangles whose sides grow at possibly different rate. The present paper establishes the existence of scaling...

The paper considers the block sampling method for long-range dependent processes. Our theory generalizes earlier ones by Hall et al. (1998) [11] on functionals of Gaussian processes and Nordman and Lahiri (2005) [16] on linear processes. In particular, we allow nonlinear transforms of linear...

We consider continuous-time random interlacements on Zd, d≥3, and investigate the percolation model where a site x of Zd is occupied if the total amount of time spent at x by all the trajectories of the interlacement at level u≥0 exceeds some constant α≥0, and empty otherwise. We also...