Asymptotic error for the Milstein scheme for SDEs driven by continuous semimartingales

DOI10.1214/105051605000000520zbMath1114.60050arXivmath/0602465OpenAlexW2004138591MaRDI QIDQ2496506

Liqing Yan

Publication date: 10 July 2006

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0602465

zbMATH Keywords

continuous martingaleMilstein schemeasymptotic behaviour of the normalized error processtightness results

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Monte Carlo methods (65C05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)

Related Items

On the approximation of Lévy driven Volterra processes and their integrals ⋮ Efficient discretisation of stochastic differential equations ⋮ Explicit Milstein schemes with truncation for nonlinear stochastic differential equations: convergence and its rate ⋮ The Pathwise Convergence of Approximation Schemes for Stochastic Differential Equations

Cites Work

• Weak limit theorems for stochastic integrals and stochastic differential equations
• Asymptotic error distributions for the Euler method for stochastic differential equations
• The Euler scheme for Lévy driven stochastic differential equations
• The Euler scheme with irregular coefficients
• Expansion of the global error for numerical schemes solving stochastic differential equations
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