title: Inverse Gaussian and its inverse process as the subordinators of fractional Brownian motion.
abstract: In this paper we study the fractional Brownian motion (FBM) time changed by the inverse Gaussian (IG) process and its inverse, called the inverse to the inverse Gaussian (IIG) process. Some properties of the time-changed processes are similar to those of the classical FBM, such as long-range dependence. However, one can also observe different characteristics that are not satisfied by the FBM. We study the distributional properties of both subordinators, namely, IG and IIG processes, and also that of the FBM time changed by these subordinators. We establish also the connections between the subordinated processes considered and the continuous-time random-walk model. For the application part, we introduce the simulation procedures for both processes and discuss the estimation schemes for their parameters. The effectiveness of these methods is checked for simulated trajectories.
authors.affiliation: Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, 50-370 Wrocław, Poland.
authors.forename: A
authors.initials: A
authors.lastname: Wyłomańska
authors.affiliation: Indian Institute of Management Sirmaur, Rampur Ghat - Engineering College Road, Kunja Matralion, Himachal Pradesh - 173025, India.
authors.forename: A
authors.initials: A
authors.lastname: Kumar
authors.affiliation: Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center Wroclaw, University of Science and Technology, 50-370 Wrocław, Poland.
authors.forename: R
authors.initials: R
authors.lastname: Połoczański
authors.affiliation: Department of Mathematics, Indian Institute of Technology Bombay, Mumbai-400076, India.
authors.forename: P
authors.initials: P
authors.lastname: Vellaisamy