Asymptotic behavior mix and diffusion process

San&eacute;, Ibrahima; Diatta, Raphel; Diatta, Jean Tosse AS; De Ziguinchor, Université AS

doi:10.21608/ejmaa.2025.291787.1209

Asymptotic behavior mix and diffusion process

Document Type : Regular research papers

Authors

¹ UFR/sciences technologies/Université Assane Seck de Ziguinchor/ Mathematics and Applications Laboratory.

² UFR/sciences technologies/Université Assane Seck de Ziguinchor/ Mathematics and Applications Laboratory.

10.21608/ejmaa.2025.291787.1209

Abstract

We study the asymptotic behavior of a solution of mixed differential equation driven by independent
fractional Brownian motion with Hurst index H ∈ (0; 1) and Levy process. There are several approaches to determining the large deviation principle for a family of stochastic differential equations for different types of stochastic process. To our knowledge,
no article presents the study via a large deviation principle (LDP) of stochastic differential equation controlled simultaneously by fractional Brownian motion (fBm) and Levy process and therefore we invest in it and consequently what allowed us to write this paper. The approach we have adopted here is different from that used by other authors. As in our
paper [7] we proceed by assuming the independence of fBm, standard Brownian motion and Poisson process in the first case where the drift is zero and the diffusion coefficients are equal to one and in the secondcase where the drift is non-zero. This work consists of determining the principle of large deviations by means of weak regularity of the coefficients of the stochastic differential equation in temporel distribution space.

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