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

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.

arXiv admin note: substantial text overlap with arXiv:1407.4109 by other authors

References in corpus (2)

• Generalized Hermite processes, discrete chaos and limit theorems
• Wiener integrals with respect to the Hermite random field and applications to the wave equation

Cited by in corpus (1)

• Central and Non-central Limit Theorems arising from the Scattering Transform and its Neural Activation Generalization