Convergence of the stochastic Euler scheme for locally Lipschitz coefficients

DOI10.1007/s10208-011-9101-9zbMath1253.65006arXiv0912.2609OpenAlexW2088070062MaRDI QIDQ656817

Martin Hutzenthaler, Arnulf Jentzen

Publication date: 13 January 2012

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.2609

zbMATH Keywords

weak convergencestochastic differential equationsEuler schemeMonte Carlo Euler methodone-sided Lipschitz continuous drift

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Ordinary differential equations and systems with randomness (34F05) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

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Cites Work

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• The Euler scheme with irregular coefficients
• The law of the Euler scheme for stochastic differential equations. I: Convergence rate of the distribution function
• Efficient Monte Carlo simulation of security prices
• Probability theory. A comprehensive course.
• Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise.
• An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
• The Pathwise Convergence of Approximation Schemes for Stochastic Differential Equations
• Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
• Comparing Hitting Time Behavior of Markov Jump Processes and Their Diffusion Approximations
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• Numerical Integration of Stochastic Differential Equations with Nonglobally Lipschitz Coefficients