On the characteristics of a class of Gaussian processes within the white noise space setting

TL;DR

This paper explores a specific class of Gaussian processes within the white noise space framework, including fractional Brownian motion and its derivatives, focusing on their covariance functions and mathematical properties.

Contribution

It introduces a new class of Gaussian processes characterized by special covariance functions within the white noise space setting.

Findings

Includes fractional Brownian motion and derivatives as special cases

Analyzes covariance functions of the processes

Connects to classical mathematical studies by Schoenberg, von Neumann, Krein

Abstract

Using the white noise space framework, we define a class of stochastic processes which include as a particular case the fractional Brownian motion and its derivative. The covariance functions of these processes are of a special form, studied by Schoenberg, von Neumann and Krein.