Asymptotic Behavior of Stochastic Complex Lattice Systems Driven by Superlinear Noise

被引：7
作者：
Chen, Zhang [1 ]
Wang, Bixiang [2 ]
机构：
[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China
[2] New Mexico Inst Min & Technol, Dept Math, Socorro, NM 87801 USA
来源：
JOURNAL OF THEORETICAL PROBABILITY | 2023年 / 36卷 / 03期
关键词：
Complex lattice system; Superlinear noise; Limit measure; Periodic measure; Weak mean random attractor; Tightness; PERIODIC MARKOV PROCESS; INVARIANT-MEASURES; DYNAMICAL-SYSTEMS; ATTRACTORS; EXISTENCE; EQUATIONS; UNIQUENESS; THEOREMS;
D O I：
10.1007/s10959-022-01206-9
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
This paper deals with the asymptotic behavior of complex stochastic lattice systems driven by superlinear noise. We first prove the well-posedness and the existence of weak mean random attractors of the systems. We then show the existence of periodic measures and the weak compactness of the set of all periodic measures when a parameter varies in a bounded interval. We finally examine the limiting behavior of the periodic measures and in particular prove that every limit of periodic measures of the stochastic Ginzburg-Landau lattice system must be a periodic measure of the stochastic Schrodinger lattice system.
引用
收藏
页码：1487 / 1519
页数：33
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