Adaptive Euler methods for stochastic systems with non-globally Lipschitz coefficients

DOI10.1007/s11075-021-01131-8zbMath1480.60182arXiv1805.11137OpenAlexW3171753014MaRDI QIDQ2066224

Cónall Kelly, Gabriel J. Lord

Publication date: 13 January 2022

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.11137

zbMATH Keywords

strong convergencestochastic differential equationsnon-globally Lipschitz coefficientsadaptive timesteppingsemi-implicit Euler method

Mathematics Subject Classification ID

Stochastic models in economics (91B70) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (2)

The role of adaptivity in a numerical method for the Cox-Ingersoll-Ross model ⋮ Weak variable step-size schemes for stochastic differential equations based on controlling conditional moments

Cites Work

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• Euler approximations with varying coefficients: the case of superlinearly growing diffusion coefficients
• Order-preserving strong schemes for SDEs with locally Lipschitz coefficients
• Non-normal drift structures and linear stability analysis of numerical methods for systems of stochastic differential equations
• Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
• The truncated Euler-Maruyama method for stochastic differential equations
• Almost sure stability of the Euler-Maruyama method with random variable stepsize for stochastic differential equations
• Stiffness of ODEs
• A note on tamed Euler approximations
• Convergence rates of the truncated Euler-Maruyama method for stochastic differential equations
• Adaptive timestepping for pathwise stability and positivity of strongly discretised nonlinear stochastic differential equations
• Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients
• On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients
• Adaptive Euler-Maruyama method for SDEs with nonglobally Lipschitz drift
• Adaptive time-stepping for the strong numerical solution of stochastic differential equations
• Stochastic C-stability and B-consistency of explicit and implicit Euler-type schemes
• An Introduction to Computational Stochastic PDEs
• Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
• Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
• Variable Step Size Control in the Numerical Solution of Stochastic Differential Equations
• Adaptive time-stepping strategies for nonlinear stochastic systems
• $V$-integrability, asymptotic stability and comparison property of explicit numerical schemes for non-linear SDEs
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• A Variable Stepsize Implementation for Stochastic Differential Equations
• A Fundamental Mean-Square Convergence Theorem for SDEs with Locally Lipschitz Coefficients and Its Applications

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