# Integral Representation of Generalized Grey Brownian Motion

## TL;DR

This paper presents a new integral representation for generalized grey Brownian motion, extending classical Gaussian process representations to non-Gaussian processes through stochastic differential equations.

## Contribution

It introduces a novel integral representation for non-Gaussian generalized grey Brownian motion, generalizing previous Gaussian-based results.

## Key findings

- Representation as a weighted integral of a non-Gaussian Ornstein-Uhlenbeck type process
- Extension of existing Gaussian process representation results to non-Gaussian cases
- Provides a framework for analyzing non-Gaussian stochastic processes

## Abstract

In this paper we investigate the representation of a class of non Gaussian processes, namely generalized grey Brownian motion, in terms of a weighted integral of a stochastic process which is a solution of a certain stochastic differential equation. In particular the underlying process can be seen as a non Gaussian extension of the Ornstein-Uhlenbeck process, hence generalizing the representation results of Muravlev as well as Harms and Stefanovits to the non Gaussian case.