On integrability of quadratic harnesses

TL;DR

This paper studies the integrability and moment properties of quadratic harnesses, a class of stochastic processes with specific regression and variance structures, highlighting the dependence on key parameters.

Contribution

It establishes the dependence order of finite moments on process parameters and raises questions about the optimal constants involved.

Findings

Identifies the dependence of moment finiteness on process parameters.

Raises open questions about the optimal constants for integrability.

Provides insights into the structure of quadratic harnesses.

Abstract

We investigate integrability properties of processes with linear regressions and quadratic conditional variances. We establish the right order of dependence of which moments are finite on the parameter defined below, raising the question of determining the optimal constant.