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Random integral operators related to the point processes

Andrey Dorogovtsev, Iaroslava Korenovska

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.

Random integral operators related to the point processes

Abstract

In the article we study properties of the random integral operator in whose kernel is obtained as a convolution of Gaussian density with a stationary point process.

Paper Structure

This paper contains 3 sections, 10 theorems, 44 equations.

Table of Contents

  1. Introduction
  2. Shifts of Gaussian density along a point process
  3. Properties of the integral random operator

Key Result

Theorem 2.1

Let $\Theta$ be a stationary ergodic point process on $\mathbb{R}$1 and $E|\Theta\cap\left[\left.0;1\right)\right.|<+\infty .$ Then there exists an event $\Omega_0$ of probability one such that for each $\omega\in \Omega_0$ a linear combinanations of the functions $\left\{ p_{\varepsilon}(\cdot-\the

Theorems & Definitions (22)

  • Theorem 2.1
  • proof
  • Lemma 2.1
  • proof
  • Corollary 2.1
  • Corollary 2.2
  • proof
  • Corollary 2.3
  • proof
  • Lemma 3.1
  • ...and 12 more