On moduli of continuity for local times of Gaussian processes
The authors study the sample path properties of increments in \(t\) of the local times \(L(t,x)\) of Gaussian processes with stationary increments and those of stationary Gaussian processes as well. In their study they have in view some well-known fine analytic properties of the moduli in \(t\) of the local time \(l(x,t)\) of a standard Wiener process \(\{W(t), t \geq 0\}\). Also, they present and discuss results which are analogous to some results previously obtained by Hawkes and Perkins. Finally, some results are presented and proved, which are analogous to some results of Perkins, for the local times \(L(x,t)\) of Gaussian processes \(\{X (t), t \geq 0\}\). Some of them do not seem to have been studied much before. In conclusion, upper bounds for moduli of continuity of the local times of Gaussian processes with stationary increments and for those of stationary Gaussian processes are established.
scientific article; zbMATH DE number 803374
scientific article