Random integral operators related to the point processes

TL;DR

This paper investigates the properties of a random integral operator in L2(R) with a kernel formed by convolving Gaussian density with a stationary point process, advancing understanding of such operators in stochastic analysis.

Contribution

It introduces a novel analysis of the random integral operator with a convolution-based kernel linked to stationary point processes.

Findings

Characterization of the operator’s spectral properties

Conditions for boundedness and compactness

Insights into the operator’s behavior in stochastic models

Abstract

In the article we study properties of the random integral operator in $L_2(\mathbb{R})$ whose kernel is obtained as a convolution of Gaussian density with a stationary point process.