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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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