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Limits of invariant measures of stochastic Burgers equations driven by two kinds of α-stable processes

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  • Liu, Xianming

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.

Suggested Citation

  • Liu, Xianming, 2022. "Limits of invariant measures of stochastic Burgers equations driven by two kinds of α-stable processes," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 1-21.
    • Handle: RePEc:eee:spapps:v:146:y:2022:i:c:p:1-21
    DOI: 10.1016/j.spa.2021.12.016
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    References listed on IDEAS

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    1. Zhang, Xicheng, 2013. "Derivative formulas and gradient estimates for SDEs driven by α-stable processes," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1213-1228.
    2. Wang, Ran & Xu, Lihu, 2018. "Asymptotics for stochastic reaction–diffusion equation driven by subordinate Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1772-1796.
    3. Z. Dong, 2008. "On the Uniqueness of Invariant Measure of the Burgers Equation Driven by Lévy Processes," Journal of Theoretical Probability, Springer, vol. 21(2), pages 322-335, June.
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