Asymptotic behavior mix and diffusion process | ||
| Electronic Journal of Mathematical Analysis and Applications | ||
| Article 6, Volume 13, Issue 2, 2025, Pages 1-9 PDF (505.39 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/ejmaa.2025.291787.1209 | ||
| Authors | ||
| Ibrahima Sané* 1; Raphel Diatta2; Jean Tosse AS Diatta2; Université AS de Ziguinchor2 | ||
| 1UFR/sciences technologies/Université Assane Seck de Ziguinchor/ Mathematics and Applications Laboratory. | ||
| 2UFR/sciences technologies/Université Assane Seck de Ziguinchor/ Mathematics and Applications Laboratory. | ||
| 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. | ||
| Keywords | ||
| Fractional Brownian motion; Levy process; Large deviation principle; Mixed stochastic differential equation | ||
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