Tempered Fractional Brownian Motion with Variable Index and Variable Tempering Parameter

TL;DR

This paper explores advanced generalizations of tempered fractional Brownian motion, including models with multiple and variable indices and tempering parameters, expanding the theoretical framework of fractional stochastic processes.

Contribution

It introduces new models of tempered fractional Brownian motion with variable indices and tempering parameters, extending existing theories to more flexible and complex stochastic processes.

Findings

Developed models with multiple indices and variable parameters.

Extended the theoretical understanding of tempered fractional Brownian motion.

Provided a foundation for future applications in complex stochastic modeling.

Abstract

Generalizations of tempered fractional Brownian from single index to two indices and variable index or tempered multifractional Brownian motion are studied. Tempered fractional Brownian motion and tempered multifractional Brownian motion with variable tempering parameter are considered.