Generalized Hermite process: tempering, properties and applications

TL;DR

This paper introduces a tempered version of the generalized Hermite process by modifying its kernel with an exponential factor, studying its properties and applying it to non-parametric regression.

Contribution

It proposes a new tempered Hermite process, extending the classical process with an exponential tempering factor, and explores its properties and applications.

Findings

The tempered process is well-defined for positive tempering parameter.

Properties such as stationarity and self-similarity are analyzed.

Application to non-parametric regression demonstrates practical utility.

Abstract

In this work, we introduce a new process by modifying the kernel in the time domain representation of the generalized Hermite process. This modification is constructed by means of multiplication of the kernel in the time definition of the process by an exponential tempering factor {\lambda} > 0 such that this new process is well defined. Several properties of the process are studied and an application to non-parametric regression is also given.