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Large deviation of generalized fractional Brownian motion and its application
https://doi.org/10.26907/0021-3446-2025-11-13-28
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.
About the Authors
H. Ahalli
Mohammed I University Oujda Rankings
Morocco
Morocco
Hajar Ahalli
BP 524 BV Mohammed VI, Oujda, 60000
A. Aslimani
Mohammed I University Oujda Rankings
Morocco
Morocco
Abderrahim Aslimani
BP 524 BV Mohammed VI, Oujda, 60000
S. Moussaten
Mohammed I University Oujda Rankings
Morocco
Morocco
Soufiane Moussaten
BP 524 BV Mohammed VI, Oujda, 60000
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Review
For citations:
Ahalli H., Aslimani A., Moussaten S. Large deviation of generalized fractional Brownian motion and its application. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2025;(11):13-28. (In Russ.) https://doi.org/10.26907/0021-3446-2025-11-13-28
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