کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1156718 | 958860 | 2013 | 27 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Ergodicity of the stochastic real Ginzburg–Landau equation driven by αα-stable noises Ergodicity of the stochastic real Ginzburg–Landau equation driven by αα-stable noises](/preview/png/1156718.png)
We study the ergodicity of the stochastic real Ginzburg–Landau equation driven by additive αα-stable noises, showing that as α∈(3/2,2)α∈(3/2,2), this stochastic system admits a unique invariant measure. After establishing the existence of invariant measures by the same method as in Dong et al. (2011) [12], we prove that the system is strong Feller and accessible to zero. These two properties imply the ergodicity by a simple but useful criterion by Hairer (2008) [14]. To establish the strong Feller property, we need to truncate the nonlinearity and apply a gradient estimate established by Priola and Zabczyk (2011) [22] (or see Priola et al. (2012) [20] for a general version for the finite dimension systems). Because the solution has discontinuous trajectories and the nonlinearity is not Lipschitz, we cannot solve a control problem to get irreducibility. Alternatively, we use a replacement, i.e., the fact that the system is accessible to zero. In Section 3, we establish a maximal inequality for stochastic αα-stable convolution, which is crucial for studying the well-posedness, the strong Feller property and the accessibility of the mild solution. We hope this inequality will also be useful for studying other SPDEs forced by αα-stable noises.
Journal: Stochastic Processes and their Applications - Volume 123, Issue 10, October 2013, Pages 3710–3736