Explicit multiscale numerical method for super-linear slow-fast stochastic differential equations

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Cui, Yuanping and Li, Xiaoyue and Mao, Xuerong (2025) Explicit multiscale numerical method for super-linear slow-fast stochastic differential equations. Stochastic Processes and their Applications. ISSN 0304-4149 (https://doi.org/10.1016/j.spa.2025.104653)

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Abstract

This manuscript is dedicated to the numerical approximation of super-linear slow-fast stochastic differential equations (SFSDEs). Borrowing the heterogeneous multiscale idea, we propose an explicit multiscale Euler–Maruyama scheme suitable for SFSDEs with locally Lipschitz coefficients using an appropriate truncation technique. By the averaging principle, we establish the strong convergence of the numerical solutions to the exact solutions in the th moment. Additionally, under lenient conditions on the coefficients, we also furnish a strong error estimate. In conclusion, we give two illustrative examples and accompanying numerical simulations to affirm the theoretical outcomes.

ORCID iDs

Cui, Yuanping, Li, Xiaoyue and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
  • Item type:Article
    ID code:92636
    Dates:
    Date
    Event
    13 April 2025
    Published
    13 April 2025
    Published Online
    1 April 2025
    Accepted
    11 February 2025
    Submitted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:17 Apr 2025 15:13
    Last modified:18 Apr 2025 00:20
    URI:https://strathprints.strath.ac.uk/id/eprint/92636
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