作者：de Bouard, A.; Gazeau, M.
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：In this article we propose a generalization of the theory of diffusion approximation for random ODE to a nonlinear system of random Schrodinger equations. This system arises ill the study of pulse propagation in randomly birefringent optical fibers. We first show existence and uniqueness of solutions for the random PDE and the limiting equation. We follow the work of Gamier and Marty [Wave Motion 43 (2006) 544-560], Marty [Problemes d'evolution en milieux aleatoires: Theoremes limites, schemas...
作者：Zhang, Xicheng
作者单位：Wuhan University
摘要：In this article we study a class of stochastic functional differential equations driven by Levy processes (in particular, alpha-stable processes), and obtain the existence and uniqueness of Markov solutions in small time intervals. This corresponds to the local solvability to a class of quasi-linear partial integro-differential equations. Moreover, in the constant diffusion coefficient case, without any assumptions on the Levy generator, we also show the existence of a unique maximal weak solu...
