Bounds for the expected number of level crossings of certain harmonizable infinitely divisible processes
Let \(\{X(t)\), \(t\in [0,1]\}\) be a complex-valued strongly stationary harmonizable \(\xi_g\)-radial process. The authors study stationary harmonizable infinitely divisible processes of the form \(Y(t)=\hbox {Re}\{X(t)\}\). Let \(N_u(0,1)\) be the number of crossings of a level \(u\) by \(Y(t)\) on \([0,1]\). Equivalent upper and lower bounds for \(EN_0(0,1)\) are derived and cruder bounds are presented for \(EN_u(0,1)\) for an arbitrary level \(u\). A limit for \(EN_u(0,1)\) is given as \(u\to \infty \).
harmonizable infinitely divisible process
scientific article; zbMATH DE number 1364484
scientific article