# Time-changed fractional Ornstein-Uhlenbeck process

## TL;DR

This paper introduces a time-changed fractional Ornstein-Uhlenbeck process, analyzing its moments, density existence, and deriving a generalized Fokker-Planck equation to describe its behavior.

## Contribution

It presents a novel combination of fractional Ornstein-Uhlenbeck processes with inverse subordinators, extending the understanding of their properties and density functions.

## Key findings

- Moments of the process are characterized.
- Existence of the probability density is established.
- A generalized Fokker-Planck equation is derived.

## Abstract

We define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.