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Uniform in time convergence of numerical schemes for stochastic differential equations via Strong Exponential stability: Euler methods, Split-Step and Tamed Schemes
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We prove a general criterion providing sufficient conditions under which a time-discretiziation of a given Stochastic Differential Equation (SDE) is a uniform in time approximation of the SDE. The criterion is also, to a certain extent, discussed in the paper, necessary. Using such a criterion we then analyse the convergence properties of numerical methods for solutions of SDEs; we consider Explicit and Implicit Euler, split-step and (truncated) tamed Euler methods. In particular, we show that, under mild conditions on the coefficients of the SDE (locally Lipschitz and strictly monotonic), these methods produce approximations of the law of the solution of the SDE that converge uniformly in time. The theoretical results are verified by numerical examples.
Forward citations
Cited by 2 Pith papers
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Long time strong convergence analysis of one-step methods for McKean-Vlasov SDEs with superlinear growth coefficients
For contractive McKean-Vlasov SDEs with superlinear drift and diffusion, the projected Euler and backward Euler schemes converge in mean square at rate 1/2 uniformly in time.
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Strong convergence in the infinite horizon of numerical methods for stochastic delay differential equations
A general four-condition patching argument gives time-uniform strong error bounds for SDDE numerical methods, applied to backward and truncated Euler-Maruyama methods and to invariant measures.
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