International Journal of Nonlinear Analysis and Applications

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

Document Type : Review articles

Authors

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

Abstract

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.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 6
June 2025
Pages 161-171
  • Receive Date: 27 January 2022
  • Revise Date: 15 February 2023
  • Accept Date: 03 May 2024