Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations

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This article introduces and analyzes a new explicit, easily implementable, and full discrete accelerated exponential Euler-type approximation scheme for additive space-time white noise driven stochastic partial differential equations (SPDEs) with possibly non-globally monotone nonlinearities such as stochastic Kuramoto-Sivashinsky equations.

• The main result of this article proves that the proposed approximation scheme converges strongly and numerically weakly to the solution process of such an SPDE.
• Key ingredients in the proof of our convergence result are a suitable generalized coercivity-type condition, the specific design of the accelerated exponential Euler-type approximation scheme, and an application of Fernique's theorem.