Strong convergence of the stopped Euler-Maruyama method for nonlinear stochastic differential equations

DOI10.1016/j.amc.2013.08.023zbMath1329.65018OpenAlexW2065848595MaRDI QIDQ907562

Wei Liu, Xuerong Mao

Publication date: 25 January 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2013.08.023

zbMATH Keywords

strong convergencestopping timenonlinear SDEsstopped Euler-Maruyama method

Mathematics Subject Classification ID

Numerical solutions to stochastic differential and integral equations (65C30)

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Cites Work

• A weak trapezoidal method for a class of stochastic differential equations
• Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
• A variable step-size control algorithm for the weak approximation of stochastic differential equations
• Numerical solutions of stochastic differential delay equations under the generalized Khasminskii-type conditions
• Preserving positivity in solutions of discretised stochastic differential equations
• A highly sensitive mean-reverting process in finance and the Euler-Maruyama approximations
• Pathwise approximation of stochastic differential equations on domains: Higher order convergence rates without global Lipschitz coefficients
• Higher-order implicit strong numerical schemes for stochastic differential equations
• A note on Euler's approximations
• The optimal uniform approximation of systems of stochastic differential equations
• Projection scheme for stochastic differential equations with convex constraints.
• Stopped diffusion processes: boundary corrections and overshoot
• Exact approximation rate of killed hypoelliptic diffusions using the discrete Euler scheme
• Stochastic ordinary differential equations in applied and computational mathematics
• Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
• Numerical Integration of Multiplicative-Noise Stochastic Differential Equations
• Convergence of discretized stochastic (interest rate) processes with stochastic drift term
• Balanced Implicit Methods for Stiff Stochastic Systems
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• Predictor-Corrector Methods of Runge--Kutta Type for Stochastic Differential Equations
• A Variable Stepsize Implementation for Stochastic Differential Equations
• The tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients
• Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence
• Stepsize Control for Mean-Square Numerical Methods for Stochastic Differential Equations with Small Noise
• Numerical Integration of Stochastic Differential Equations with Nonglobally Lipschitz Coefficients
• Stochastic differential equations. An introduction with applications.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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