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Duc-Trong Luong

Publications and source records attributed to Duc-Trong Luong.

4 recordsLinked to original sources
arXiv2025

A tamed-adaptive Milstein scheme for stochastic differential equations with low regularity coefficients

We propose a tamed-adaptive Milstein scheme for stochastic differential equations in which the first-order derivatives of the coefficients are locally Hölder continuous of order $α$. We show that the scheme converges in the $L_2$-norm with a rate of $(1+α)/2$ over both finite intervals $[0, T]$ and the infinite interval $(0, +\infty)$, under certain growth conditions on the coefficients.

math.PR↗
arXiv2024

A Multi-level Monte Carlo simulation for invariant distribution of Markovian switching Lévy-driven SDEs with super-linearly growth coefficients

This paper concerns the numerical approximation for the invariant distribution of Markovian switching Lévy-driven stochastic differential equations. By combining the tamed-adaptive Euler-Maruyama scheme with the Multi-level Monte Carlo method, we propose an approximation scheme that can be applied to stochastic differential equations with super-linear growth drift and diffusion coefficients.

math.PR↗
arXiv2024

On the infinite time horizon approximation for Lévy-driven McKean-Vlasov SDEs with non-globally Lipschitz continuous and super-linearly growth drift and diffusion coefficients

This paper studies the numerical approximation for McKean-Vlasov stochastic differential equations driven by Lévy processes. We propose a tamed-adaptive Euler-Maruyama scheme and consider its strong convergence in both finite and infinite time horizons when applying for some classes of Lévy-driven McKean-Vlasov stochastic differential equations with non-globally Lipschitz continuous and super-linearly growth drift and diffusion coefficients.

math.PR↗