Tamed Milstein Scheme for Stochastic Differential Equations with Markovian Switching with Super-linear Drift and Diffusion Coefficients

Tejinder Kumar

doi:10.1016/j.cam.2025.117306

Tamed Milstein Scheme for Stochastic Differential Equations with Markovian Switching with Super-linear Drift and Diffusion Coefficients

Tejinder Kumar^*

^*Corresponding author for this work

School of Engineering Physics and Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

We introduce a tamed Milstein scheme for stochastic differential equations with Markovian switching, specifically tailored for cases where both the drift and diffusion coefficients exhibit super-linear growth. We establish the moment stability of the proposed scheme and prove that it achieves a strong convergence rate of 1.0 in the Lp-sense, even when the coefficients are non-globally Lipschitz and grow super-linearly.

Original language	English
Article number	117306
Pages (from-to)	1-17
Number of pages	17
Journal	Journal of Computational and Applied Mathematics
Volume	481
Early online date	22 Dec 2025
DOIs	https://doi.org/10.1016/j.cam.2025.117306
Publication status	Published - 1 Aug 2026

Keywords

Milstein scheme
tamed scheme
super-linear coefficients
rate of convergence
Markovian switching
Super-linear coefficients
65C30
Tamed scheme
Rate of convergence

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10.1016/j.cam.2025.117306Licence: CC BY

1-s2.0-S0377042725008180-mainAccepted author manuscript, 2.66 MBLicence: CC BY
1-s2.0-S0377042725008180-main (1)Final published version, 3.34 MBLicence: CC BY

Cite this

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abstract = "We introduce a tamed Milstein scheme for stochastic differential equations with Markovian switching, specifically tailored for cases where both the drift and diffusion coefficients exhibit super-linear growth. We establish the moment stability of the proposed scheme and prove that it achieves a strong convergence rate of 1.0 in the Lp-sense, even when the coefficients are non-globally Lipschitz and grow super-linearly.",

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N2 - We introduce a tamed Milstein scheme for stochastic differential equations with Markovian switching, specifically tailored for cases where both the drift and diffusion coefficients exhibit super-linear growth. We establish the moment stability of the proposed scheme and prove that it achieves a strong convergence rate of 1.0 in the Lp-sense, even when the coefficients are non-globally Lipschitz and grow super-linearly.

AB - We introduce a tamed Milstein scheme for stochastic differential equations with Markovian switching, specifically tailored for cases where both the drift and diffusion coefficients exhibit super-linear growth. We establish the moment stability of the proposed scheme and prove that it achieves a strong convergence rate of 1.0 in the Lp-sense, even when the coefficients are non-globally Lipschitz and grow super-linearly.

KW - Milstein scheme

KW - tamed scheme

KW - super-linear coefficients

KW - rate of convergence

KW - Markovian switching

KW - Super-linear coefficients

KW - 65C30

KW - Tamed scheme

KW - Rate of convergence

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DO - 10.1016/j.cam.2025.117306

M3 - Article

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JF - Journal of Computational and Applied Mathematics

M1 - 117306

ER -

Tamed Milstein Scheme for Stochastic Differential Equations with Markovian Switching with Super-linear Drift and Diffusion Coefficients

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Keywords

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