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Averaging principle for stochastic real Ginzburg-Landau equation driven by $ \alpha $-stable process

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Xiaobin Sun is supported by the National Natural Science Foundation of China (11601196, 11771187, 11931004), the NSF of Jiangsu Province (No. BK20160004) and the Priority Academic Program Development of Jiangsu Higher Education Institutions. Jianliang Zhai is supported by the National Natural Science Foundation of China (11431014, 11671372, 11721101), the Fundamental Research Funds for the Central Universities (No. WK0010450002, WK3470000008), Key Research Program of Frontier Sciences, CAS, No: QYZDB-SSW-SYS009, School Start-up Fund (USTC) KY0010000036

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  • In this paper, we study a system of stochastic partial differential equations with slow and fast time-scales, where the slow component is a stochastic real Ginzburg-Landau equation and the fast component is a stochastic reaction-diffusion equation, the system is driven by cylindrical $ \alpha $-stable process with $ \alpha\in (1, 2) $. Using the classical Khasminskii approach based on time discretization and the techniques of stopping times, we show that the slow component strong converges to the solution of the corresponding averaged equation under some suitable conditions.

    Mathematics Subject Classification: Primary: 35R60; Secondary: 60H15.


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