ON THE QHASI CLASS AND ITS EXTENSION TO SOME GAUSSIAN SHEETS

Abstract

Introduced in 2018 the generalized bifractional Brownian motion is considered as an element of the quasi-helix with approximately stationary increment class of real centered Gaussian processes conditioning by parameters. This paper proves that the generalized bifractional Brownian motion is an element of the above mentioned class with no condition on parameters. The quasi-helix with approximately stationary increment class of real centered Gaussian processes is extended to two-dimensional processes as the fractional Brownian sheet, the sub-fractional Brownian sheet, and the bifractional Brownian sheet. This generalized presentation of the class of stochastic processes is used to augment the training samples for generative adversarial networks in computer vision problem.