Local times for multifractional square Gaussian processes

TL;DR

This paper studies a class of multifractional Gaussian processes defined via double Ito--Wiener integrals, establishing their continuity and existence of square integrable local times, thus extending understanding of their sample path properties.

Contribution

It introduces a new class of multifractional processes and proves their continuity and local time properties, generalizing previous results on Rosenblatt processes.

Findings

Process is continuous almost surely

Existence of square integrable local time

Generalization of multifractional Rosenblatt process

Abstract

We consider multifractional process given by double Ito--Wiener integrals, which generalize the multifractional Rosenblatt process. We prove that this process is continuous and has a square integrable local time.