带乘性Lévy噪声的随机Cahn-Hilliard方程的中偏差原理  

Moderate deviation principle for stochastic Cahn-Hilliard equations with multiplicative Lévy noise

作　　者：王颖 陈光淦 汪品 WANG Ying;CHEN Guang-Gan;WANG Pin(School of Mathematical Sciences/V.C.&V.R.Key Lab,Sichuan Normal University,Chengdu 610068,China)

机构地区：[1]四川师范大学数学科学学院/可视化计算与虚拟现实四川省重点实验室,成都610068

出　　处：《四川大学学报（自然科学版）》2022年第6期13-22,共10页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(12171343);四川省科技计划项目(2022JDTD0019)。

摘　　要：中偏差原理是统计推断理论中构建渐近置信区间的重要依据之一.本文旨在研究带乘性Lévy噪声的随机Cahn-Hilliard方程的中偏差原理.在该方程中,带跳噪声和高阶非线性项的耦合导致随机积分的计算较为复杂,不易获得指数型概率估计.本文运用经典弱收敛方法逐一验证了两个中偏差条件,进而建立了方程的中偏差原理.Moderate deviation principle is an important method for constructing asymptotic confidence intervals in statistical inference. This work aims at the moderate deviation principle for the stochastic Cahn-Hilliard equations driven by multiplicative Lévy noise. In these equations, the interaction of high order nonlinear terms and jump noises results in the difficulty of dealing with the stochastic integrals and deducing the exponential-type probability estimates. With the help of classical weak convergence method, we establish the moderate deviation principle underlying the verification of two moderate deviation conditions.

关 键 词：中偏差原理 随机Cahn-Hilliard方程 泊松随机测度 弱收敛准则 

分 类 号：O175.2[理学—数学]