The Large Deviation of Generalized Fractional Brownian Motion and Application

Abstract

In this paper, we investigate the large deviations of the local time of a self-similar Gaussian process called the generalized fractional Brownian motion process. This process, introduced by Zili [4], as an extension of the subfractional Brownian motion and fractional Brownian motion Gaussian processes, represents a significant breakthrough in stochastic processes. It provides a more flexible and robust approach to modeling natural phenomena and complex systems. Our study starts by presenting the large deviation estimates for the local time of this process. Additionally, we establish the law of iterated logarithm for the corresponding local time, further enhancing our understanding of its behavior.