an:06646911
Zbl 1387.60102
Pei, Bin; Xu, Yong; Wu, Jiang-Lun
Two-time-scales hyperbolic-parabolic equations driven by Poisson random measures: existence, uniqueness and averaging principles
EN
J. Math. Anal. Appl. 447, No. 1, 243-268 (2017).
00360266
2017
j
60H15 35R60 35M33
averaging principles; stochastic hyperbolic-parabolic equations; Poisson random measures; two-time-scales
Summary: In this article, we are concerned with averaging principle for stochastic hyperbolic-parabolic equations driven by Poisson random measures with slow and fast time-scales. We first establish the existence and uniqueness of weak solutions of the stochastic hyperbolic-parabolic equations. Then, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the stochastic wave equation is an average with respect to the stationary measure of the fast varying process. Finally, we derive the rate of strong convergence for the slow component towards the solution of the averaged equation.