Large deviation principle for a mixed fractional, jump and local process

نویسندگان
Diedhiou, Alassane ID 1
Sane, Ibrahima ID 2
Diatta, Raphael ID 3
Manga, Clément ID 4

1 Université Assane Seck, Département de Mathématiques, Laboratoire Mathématiques et Applications, B.P. 523, Ziguinchor, Sénégal

2 Université Assane Seck, Département de Mathématiques, Laboratoire Mathématiques et Applications, B.P. 523, Ziguinchor, Sénégal

3 Université Assane Seck, Département de Mathématiques, Laboratoire Mathématiques et Applications, B.P. 523, Ziguinchor, Sénégal

4 Université Assane Seck, Département de Mathématiques, Laboratoire Mathématiques et Applications, B.P. 523, Ziguinchor, Sénégal

doi
10.22075/ijnaa.2024.26073.3218
چکیده

We study the asymptotic behavior of a solution of a mixed differential equation driven by an independent fractional Brownian motion with Hurst index $H\in (0; 1)$ and compensated Poisson process and a local time. This study consists in determining the uniform Freidlin-Wentzell estimates in a temporal distribution space $\mathcal{S'(\mathbb{R})}$. The approach is purely probabilistic.

کلیدواژه‌ها
Large deviations principle, Fractional Brownian motion, Principle contraction, Poisson process, Skorohod problem