Real harmonizable multifractional stable process and its local properties

TL;DR

This paper introduces a new class of stochastic processes called real harmonizable multifractional stable processes, analyzing their local properties, regularity, and existence of local time.

Contribution

It defines the process, proves its H"older continuity and localizability, and establishes the existence and regularity of its local time.

Findings

Proved H"older continuity of the process

Established localizability of the process

Showed existence and regularity of local time

Abstract

A real harmonizable multifractional stable process is defined, its H\"older continuity and localizability are proved. The existence of local time is shown and its regularity is established.