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Register a new userStrong and weak convergence rates for slow-fast stochastic differential equations driven by $alpha$-stable process
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In this paper, we study the averaging principle for a class of stochastic differential equations driven by $alpha$-stable processes with slow and fast time-scales, where $alphain(1,2)$. We prove that the strong and weak convergence order are $1-1/alpha$ and $1$ respectively. We show, by a simple example, that $1-1/alpha$ is the optimal strong convergence rate.
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In this paper, we consider the averaging principle for a class of McKean-Vlasov stochastic differential equations with slow and fast time-scales. Under some proper assumptions on the coefficients, we first prove that the slow component strongly converges to the solution of the corresponding averaged equation with convergence order $1/3$ using the approach of time discretization. Furthermore, under stronger regularity conditions on the coefficients, we use the technique of Poisson equation to improve the order to $1/2$, which is the optimal order of strong convergence in general.
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, 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.
A large deviation principle is derived for stochastic partial differential equations with slow-fast components. The result shows that the rate function is exactly that of the averaged equation plus the fluctuating deviation which is a stochastic partial differential equation with small Gaussian perturbation. This also confirms the effectiveness of the approximation of the averaged equation plus the fluctuating deviation to the slow-fast stochastic partial differential equations.
This paper is devoted to proving the strong averaging principle for slow-fast stochastic partial differential equations with locally monotone coefficients, where the slow component is a stochastic partial differential equations with locally monotone coefficients and the fast component is a stochastic partial differential equations (SPDEs) with strongly monotone coefficients. The result is applicable to a large class of examples, such as the stochastic porous medium equation, the stochastic $p$-Laplace equation, the stochastic Burgers type equation and the stochastic 2D Navier-Stokes equation, which are the nonlinear stochastic partial differential equations. The main techniques are based on time discretization and the variational approach to SPDEs.
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