Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities

Abstract

In this article we propose a new, explicit and easily implementable numerical method for approximating a class of semilinear stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. We establish strong convergence rates for this approximation method in the case of semilinear stochastic evolution equations with globally monotone coefficients. Our strong convergence result, in particular, applies to a class of stochastic reaction-diffusion partial differential equations.

38 pages

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Cited by in corpus (17)

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• On the discretisation in time of the stochastic Allen-Cahn equation
• Analysis of Some Splitting Schemes for the Stochastic Allen-Cahn Equation
• Weak convergence rates for an explicit full-discretization of stochastic Allen-Cahn equation with additive noise
• Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations
• Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations
• On strong $L^2$ convergence of time numerical schemes for the stochastic 2D Navier-Stokes equations
• Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations
• Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions
• Exponential moments for numerical approximations of stochastic partial differential equations
• Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities
• Adaptive time-stepping for Stochastic Partial Differential Equations with non-Lipschitz drift
• Error estimates of semi-discrete and fully discrete finite element methods for the Cahn-Hilliard-Cook equation
• On the Itô-Alekseev-Gröbner formula for stochastic differential equations
• Strong convergence for explicit space-time discrete numerical approximation for 2D stochastic Navier-Stokes equations
• Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus
• Exponential moment bounds and strong convergence rates for tamed-truncated numerical approximations of stochastic convolutions