Limits of invariant measures of stochastic Burgers equations driven by two kinds of α-stable processes
Limits of invariant measures of stochastic Burgers equations driven by two kinds of α-stable processes
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DOI：
10.1016/j.spa.2021.12.016
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发表时间：
2022-01
影响因子：
1.4
通讯作者：
Xianming Liu
中科院分区：
文献类型：
--
作者：
Xianming Liu
本文研究了环面上两类柱α-稳定过程（即柱从属布朗运动和从属柱布朗运动）驱动的随机Burgers方程的不变概率测度在α→ 2时的收敛性.证明了在Wasserstein距离下，由圆柱从属布朗运动或从属圆柱布朗运动驱动的随机Burgers方程的不变概率测度收敛于由圆柱布朗运动驱动的随机Burgers方程的不变概率测度.这一结果表明了非高斯噪声随机动力系统与高斯噪声随机动力系统之间的联系。
In this work, we study the convergence behavior, as α→ 2, of the invariant probability measures of stochastic Burgers equations driven by two kinds of cylindrical α-stable processes (ie, cylindrical subordinated Brownian motions and subordinated cylindrical Brownian motions) on torus. We prove that the invariant probability measures of stochastic Burgers equations driven by cylindrical subordinated Brownian motions or subordinated cylindrical Brownian motions converge to the invariant probability measure of stochastic Burgers equations forced by cylindrical Brownian motions in Wasserstein distance. This result shows a connection between stochastic dynamical systems with non-Gaussian noises and stochastic dynamical systems with Gaussian noises.