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Stabilized explicit methods for the approximation of stochastic systems driven by small additive noises

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  • de la Cruz, H.

Abstract

We develop an approach for the construction of stable numerical schemes for the strong approximation of stochastic differential systems with small additive noises. Explicit integrators with valuable stability properties are proposed and their mean-square convergence is studied. Computer simulations are carry out to illustrate the practical performance of the methods and their advantages in comparison with other existing integrators.

Suggested Citation

  • de la Cruz, H., 2020. "Stabilized explicit methods for the approximation of stochastic systems driven by small additive noises," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305919
    DOI: 10.1016/j.chaos.2020.110195
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    References listed on IDEAS

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    1. Rydén, Tobias & Wiktorsson, Magnus, 2001. "On the simulation of iterated Itô integrals," Stochastic Processes and their Applications, Elsevier, vol. 91(1), pages 151-168, January.
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    Cited by:

    1. D'Ambrosio, Raffaele & de la Cruz, Hugo & Scalone, Carmela, 2024. "A Magnus-based integrator for Brownian parametric semi-linear oscillators," Applied Mathematics and Computation, Elsevier, vol. 472(C).
    2. Zhang, Meng & Zhu, Quanxin, 2022. "Finite-time input-to-state stability of switched stochastic time-varying nonlinear systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Juan-Carlos Cortés & Elena López-Navarro & José-Vicente Romero & María-Dolores Roselló, 2021. "Approximating the Density of Random Differential Equations with Weak Nonlinearities via Perturbation Techniques," Mathematics, MDPI, vol. 9(3), pages 1-17, January.

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