Regularization and integral representations of Hermite processes (Q613203)

It is known that Hermite processes have a finite-time interval representation. For the fractional Brownian motion, the representation is well known and plays a fundamental role in developing the stochastic calculus for the process. For the Rosenblatt process, the finite-time interval representation was originally established by using cumulants. The representation was extended to general Hermite processes through the convergence of suitable partial sum processes. In the paper, an alternative proof is provided for the finite-time interval representation of Hermite processes. The approach is based on the regularization of Hermite processes and the fractional Gaussian noises underlying them, and uses neither cumulants nor convergence of partial sums.