Abstract
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 (i.e., 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.
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