Wiener integrals with respect to the two-parameter tempered Hermite random fields

TL;DR

This paper develops the foundational theory of two-parameter tempered Hermite fields, including their representations, properties, and stochastic integration, extending the classical Hermite field framework with exponential tempering.

Contribution

It introduces the two-parameter tempered Hermite field and establishes its basic properties and stochastic integration theory, which were not previously developed.

Findings

Established moving average and spectral representations.

Analyzed sample path properties.

Developed Wiener stochastic integration for the field.

Abstract

The two-parameter tempered Hermite field modifies the power law kernel in the moving average representation of the Hermite field by adding an exponential tempering. This paper develops the basic theory of two-parameter tempered Hermite field, including moving average, sample path properties, spectral representations and the theory of Wiener stochastic integration with respect to the two-parameter tempered Hermite field of order one.