Coupling homogenization and large deviations, with applications to nonlocal parabolic partial differential equations.

Consider the following nonlocal integro-differential operator of Lévy-type L^α_ε,δ given by... related to stochastic differential equations driven by multiplicative isotropic α -stable Lévy noise (1 < α < 2). We study by using homogenization theory the behavior of u^ε,δ: R d ⟶ R of double perturbed Kolmogorov, Petrovskii and Piskunov (KPP)-type with periodic coefficients varying over length scale δ and nonlinear reaction term of scale 1 / ε,... The behavior is required as ε, δ both tend to 0. Our homogenization method is probabilistic. Since δ and ε go at the same rate, we may apply the large deviations principle with homogenized coefficients. [ABSTRACT FROM AUTHOR]