We are concerned with homogenization of stochastic differential equations (SDE) with stationary coefficients driven by Poisson random measures and Brownian motions in the critical case, that is when the limiting equation admits both a Brownian part as well as a pure jump part. We state an annealed convergence theorem. This problem is deeply connected with homogenization of integral partial diff...

The aim of the paper is to evaluate the miss probability of a Least Recently Used (LRU) cache, when it is offered a non-stationary request process given by a Poisson cluster point process. First, we construct a probability space using Palm theory, describing how to consider a tagged document with respect to the rest of the request process. This framework allows us to derive a general integral f...