On estimation of the Orey index for a class of Gaussian processes

TL;DR

This paper extends the Orey index concept to a broader class of Gaussian processes without stationary increments and provides methods to estimate this index from discrete data, enhancing understanding of their sample path properties.

Contribution

It introduces a generalized definition of the Orey index for second order processes lacking stationary increments and proposes an estimation technique from discrete observations.

Findings

Extended the Orey index to non-stationary Gaussian processes.

Developed an estimation method for the Orey index from discrete data.

Enhanced understanding of sample path properties of broader Gaussian processes.

Abstract

Orey suggested the definition of some index for Gaussian processes with stationary increments which determines various properties of the sample paths of this process. We give an extension of the definition of the Orey index for a second order stochastic processes which may not have stationary increments and estimate the Orey index for Gaussian process from discrete observations of its sample paths.