Existence and H\"{o}lder continuity conditions for self-intersection local time of Rosenblatt process

TL;DR

This paper investigates the conditions under which the self-intersection local time of Rosenblatt processes exists and is H"{o}lder continuous, also exploring intersection and collision local times.

Contribution

It provides new existence and regularity conditions for self-intersection local times of Rosenblatt processes, extending understanding of their path properties.

Findings

Established existence conditions for self-intersection local time.

Derived H"{o}lder continuity criteria for the local time.

Analyzed intersection and collision local times cases.

Abstract

We consider the existence and H\"{o}lder continuity conditions for the self-intersection local time of Rosenblatt process. Moreover, we study the cases of intersection local time and collision local time, respectively.