On the rate of convergence of strong Euler approximation for SDEs driven by Levy processes

DOI10.1080/17442508.2017.1381095zbMath1498.60230arXiv1608.02303OpenAlexW2963340317MaRDI QIDQ5085849

Fanhui Xu, Remigijus Mikulevičius

Publication date: 30 June 2022

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.02303

zbMATH Keywords

strong solutionsstrong approximationlevy processes

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)

Related Items (14)

Hellinger and total variation distance in approximating Lévy driven SDEs ⋮ Quantifying a convergence theorem of Gyöngy and Krylov ⋮ Using Stein's method to analyze Euler-Maruyama approximations of regime-switching jump diffusion processes ⋮ Approximation of the invariant measure of stable SDEs by an Euler-Maruyama scheme ⋮ Convergence of weak Euler approximation for nondegenerate stochastic differential equations driven by point and martingale measures ⋮ On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift ⋮ The Euler-Maruyama method for S(F)DEs with Hölder drift and α-stable noise ⋮ Distribution-dependent SDEs with Hölder continuous drift and \(\alpha\)-stable noise ⋮ On the Euler-Maruyama scheme for spectrally one-sided Lévy driven SDEs with Hölder continuous coefficients ⋮ Strong convergence of the Euler-Maruyama approximation for a class of Lévy-driven SDEs ⋮ Regularity properties of jump diffusions with irregular coefficients ⋮ Approximation of heavy-tailed distributions via stable-driven SDEs ⋮ Sharpness of Lenglart's domination inequality and a sharp monotone version ⋮ Approximation of SDEs: a stochastic sewing approach

Cites Work

• On classical solutions of linear stochastic integro-differential equations
• Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift
• Pathwise uniqueness for singular SDEs driven by stable processes
• Well-posedness of the transport equation by stochastic perturbation
• The Euler scheme for Lévy driven stochastic differential equations: limit theorems.
• On the Cauchy problem for integro-differential operators in Hölder classes and the uniqueness of the martingale problem
• Pathwise uniqueness and continuous dependence for SDEs with non-regular drift
• Lévy Processes and Stochastic Calculus
• Unnamed Item

This page was built for publication: On the rate of convergence of strong Euler approximation for SDEs driven by Levy processes