Random integrals and correctors in homogenization

摘要: This paper concerns the homogenization of a one-dimensional elliptic equation with oscillatory random coefficients. It is well-known that solution to converges an effective medium in limit vanishing correlation length medium. also corrector homogenization, i.e., difference between and homogenized solution, distribution Gaussian process when correlations are sufficiently short-range. Moreover, limiting may be written as stochastic integral respect standard Brownian motion. We generalize result large class processes long-range correlations. In this setting, process, which has interpretation fractional we show longer range correlations, larger amplitude corrector. Derivations based on careful analysis integrals make use explicit expressions for solutions equation.