Abstract:
In this paper, we investigate large deviations of the local time of a self-similar Gaussian process called the generalized fractional Brownian motion process. This process, introduced by M. Zili [4] as an extension of the sub-fractional 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 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 understanding of its behavior.
Keywords:generalized fractional Brownian motion, local time, large deviation, reproducing kernel Hilbert space, law of iterated logarithm.
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