Two-time-scales hyperbolic–parabolic equations driven by Poisson random measures: Existence, uniqueness and averaging principles
Two-time-scales hyperbolic–parabolic equations driven by Poisson random measures: Existence, uniqueness and averaging principles
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DOI：
10.1016/j.jmaa.2016.10.010
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发表时间：
2017-03
影响因子：
1.3
通讯作者：
B. Pei;Yong Xu;Jiang-Lun Wu
中科院分区：
文献类型：
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作者：
B. Pei;Yong Xu;Jiang-Lun Wu
本文讨论了具有慢和快时间尺度的Poisson随机测量驱动的随机双曲抛物型方程的平均原理。我们首先证明了随机双曲抛物型方程弱解的存在唯一性。然后，在适当的条件下，我们证明了存在一个极限过程，其中快变过程被取平均，且以随机波动方程的形式出现的极限过程是关于快变过程的平稳测度的平均值。最后，我们得到了慢分量对平均方程解的强收敛速度。
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.