On time-changed Gaussian processes and their associated Fokker-Planck-Kolmogorov equations

TL;DR

This paper derives Fokker-Planck-Kolmogorov equations for time-changed Gaussian processes, including fractional Brownian motion and Ornstein-Uhlenbeck processes, with inverse stable subordinators as time-changes.

Contribution

It introduces new Fokker-Planck-Kolmogorov equations for Gaussian processes altered by inverse stable subordinators, expanding understanding of their dynamics.

Findings

Derived equations for time-changed fractional Brownian motion with variable Hurst parameter

Established equations for time-changed Ornstein-Uhlenbeck processes

Analyzed effects of inverse stable subordinators on Gaussian process dynamics

Abstract

This paper establishes Fokker-Planck-Kolmogorov type equations for time-changed Gaussian processes. Examples include those equations for a time-changed fractional Brownian motion with time-dependent Hurst parameter and for a time-changed Ornstein-Uhlenbeck process. The time-change process considered is the inverse of either a stable subordinator or a mixture of independent stable subordinators.