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Exponential ergodicity of stochastic Burgers equations driven by \(\alpha\)-stable processes. (English) Zbl 1291.35279
Summary: In this work, we prove the strong Feller property and the exponential ergodicity of stochastic Burgers equations driven by \(\alpha/2\)-subordinated cylindrical Brownian motions with \(\alpha\in(1,2)\). To prove the results, we truncate the nonlinearity and use the derivative formula for SDEs driven by \(\alpha\)-stable noises established in [X. Zhang, Stochastic Processes Appl. 123, No. 4, 1213–1228 (2013; Zbl 1261.60060)].

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
60J65 Brownian motion
35Q30 Navier-Stokes equations
37A25 Ergodicity, mixing, rates of mixing
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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