TY - JOUR
T1 - Two-time-scales hyperbolic–parabolic equations driven by Poisson random measures
T2 - Existence, uniqueness and averaging principles
AU - Pei, Bin
AU - Xu, Yong
AU - Wu, Jiang Lun
N1 - Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2017/3/1
Y1 - 2017/3/1
N2 - 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.
AB - 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.
KW - Averaging principles
KW - Poisson random measures
KW - Stochastic hyperbolic–parabolic equations
KW - Two-time-scales
UR - http://www.scopus.com/inward/record.url?scp=84994092309&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2016.10.010
DO - 10.1016/j.jmaa.2016.10.010
M3 - 文章
AN - SCOPUS:84994092309
SN - 0022-247X
VL - 447
SP - 243
EP - 268
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -