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Register a new userOrders of strong and weak averaging principle for multiscale SPDEs driven by $alpha$-stable process
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In this paper, the averaging principle is studied for a class of multiscale stochastic partial differential equations driven by $alpha$-stable process, where $alphain(1,2)$. Using the technique of Poisson equation, the orders of strong and weak convergence are given $1-1/alpha$ and $1-r$ for any $rin (0,1)$ respectively. The main results extend Wiener noise considered by Br{e}hier in [6] and Ge et al. in [17] to $alpha$-stable process, and the finite dimensional case considered by Sun et al. in [39] to the infinite dimensional case.
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In this paper, the strong averaging principle is researched for a class of H{o}lder continuous drift slow-fast SPDEs with $alpha$-stable process by the Zvonkins transformation and the classical Khasminkiis time discretization method. As applications, an example is also provided to explain our result.
In this paper, we first study the well-posedness of a class of McKean-Vlasov stochastic partial differential equations driven by cylindrical $alpha$-stable process, where $alphain(1,2)$. Then by the method of the Khasminskiis time discretization, we prove the averaging principle of a class of multiscale McKean-Vlasov stochastic partial differential equations driven by cylindrical $alpha$-stable processes. Meanwhile, we obtain a specific strong convergence rate.
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