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Strong convergence rates for long-time approximations of SDEs with non-globally Lipschitz continuous coefficients

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arxiv 2406.10582 v1 pith:ZTVC4UUS submitted 2024-06-15 math.NA cs.NAmath.PR

Xiaoming Wu , Xiaojie Wang This is my paper · ORCID
classification math.NAcs.NAmath.PR
keywords strongconvergencelipschitznon-globallylong-timeapproximationscoefficientseuler
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This paper is concerned with long-time strong approximations of SDEs with non-globally Lipschitz coefficients.Under certain non-globally Lipschitz conditions, a long-time version of fundamental strong convergence theorem is established for general one-step time discretization schemes. With the aid of the fundamental strong convergence theorem, we prove the expected strong convergence rate over infinite time for two types of schemes such as the backward Euler method and the projected Euler method in non-globally Lipschitz settings. Numerical examples are finally reported to confirm our findings.

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Cited by 3 Pith papers

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  1. Non-asymptotic Error Analysis of Explicit Modified Euler Methods for Superlinear and Non-contractive SODEs

    math.NA 2025-09 conditional novelty 7.0 of 10

    Explicit modified Euler methods for superlinear multiplicative-noise SDEs are shown to converge in W1 distance to the invariant measure with rate τ|lnτ| under contractivity at infinity.

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    The numerical invariant measure of an explicit truncated Euler–Maruyama scheme converges to the true invariant measure at order h^{1/2} in the L1-Wasserstein distance, uniformly in time, for drifts that are dissipativ...

  3. Long time strong convergence analysis of one-step methods for McKean-Vlasov SDEs with superlinear growth coefficients

    math.NA 2025-09 conditional novelty 6.0 of 10

    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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