On a Wiener-Poisson equation with rapidly fluctuating coefficients: application to large deviations

The Journal of Nonlinear Sciences and its Applications

article

Alioune Coulibaly¹  Mouhamad Mounirou Allaya² 

[1] Amadou Mahtar Mbow University of Dakar;Iba Der Thiam University of Thies

关键词: Large deviation principle;    homogenization;    Levy process;    Legendre-Fenchel transform;   

DOI  :  10.22436/jnsa.014.06.06

学科分类：社会科学、人文和艺术（综合）

来源: Shomal University

【 摘 要 】

In this paper, we deal with a stochastic differential equation with fast oscillating coefficients and with respect to a Brownian motion and a Poisson random measure. The large deviation principle of solution is established, and the effect of the highly nonlinear and locally periodic coefficients is stated. Moreover, we derive an explicit expression for the action functional when the viscosity parameter \(\varepsilon\) is of order \(1\) while the homogenization parameter \(\delta_{\varepsilon}\) tends to zero.

【 授权许可】

Unknown