  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.

Probability