On a new family of weighted Gaussian processes: an application to bat telemetry data

TL;DR

This paper introduces a new family of weighted Gaussian processes derived from branching particle systems, demonstrating their long-range dependence and applicability to real-world data modeling.

Contribution

It presents a novel family of Gaussian processes based on branching system fluctuations, highlighting their long-range dependence and non-semimartingale properties.

Findings

Processes exhibit long-range dependence and logarithmic long-range memory.

The family is not a semimartingale.

Useful for modeling real-world data.

Abstract

In this article we use a covariance function that arises from limit of fluctuations of the rescaled occupation time process of a branching particle system, to introduce a family of weighted long-range dependence Gaussian processes. In particular, we consider two subfamilies for which we show that the process is not a semimartingale, that the processes exhibit long-range dependence and have long-range memory of logarithmic order. Finally, we illustrate that this family of processes is useful for modeling real world data.