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

Coulibaly, Alioune ¹ ; Allaya, Mouhamad Mounirou ²

¹ Amadou Mahtar Mbow University of Dakar, Senegal
² Iba Der Thiam University of Thies, Senegal

Journal of nonlinear sciences and its applications, Tome 14 (2021) no. 6, p. 440-451.

Résumé

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.

Détail

DOI : 10.22436/jnsa.014.06.06

Classification : 35B27, 35K57, 60F10, 60H15
Keywords: Large deviation principle, homogenization, Levy process, Legendre-Fenchel transform

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