Generalized Hermite process: tempering, properties and applications

Abstract: In this work, we introduce a new process by modifying the kernel in the time domain representation of the generalized Hermite process. This modification is constructed by means of multiplication of the kernel in the time definition of the process by an exponential tempering factor {\lambda} > 0 such that this new process is well defined. Several properties of the process are studied and an application to non-parametric regression is also given.