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• W2963352008 abstract "In this paper, we derive a strong convergence rate of spatial finite difference approximations for both focusing and defocusing stochastic cubic Schrödinger equations driven by a multiplicative Q-Wiener process. Beyond the uniform boundedness of moments for high order derivatives of the exact solution, the key requirement of our approach is the exponential integrability of both the exact and numerical solutions. By constructing and analyzing a Lyapunov functional and its discrete correspondence, we derive the uniform boundedness of moments for high order derivatives of the exact solution and the first order derivative of the numerical solution, which immediately yields the well-posedness of both the continuous and discrete problems. The latter exponential integrability is obtained through a variant of a criterion given by Cox, Hutzenthaler and Jentzen [arXiv:1309.5595]. As a by-product of this exponential integrability, we prove that the exact and numerical solutions depend continuously on the initial data and obtain a large deviation-type result on the dependence of the noise with first order strong convergence rate." @default.
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• W2963352008 date "2017-10-01" @default.
• W2963352008 modified "2023-10-18" @default.
• W2963352008 title "Strong convergence rate of finite difference approximations for stochastic cubic Schrödinger equations" @default.
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• W2963352008 doi "https://doi.org/10.1016/j.jde.2017.05.002" @default.
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