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This paper proposes an adaptive timestep construction for an Euler-Maruyama approximation of SDEs with a drift which is not globally Lipschitz.
Numerical Solution of Stochastic Differential Equations
P.E. Kloeden and E. Platen · 1992
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Variable step size control in the numerical solution of stochastic differential equations
J.G. Gaines and T.J. Lyons · 1997
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Stochastic Differential Equations and Applications
X. Mao · 1997
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Step size control in the numerical solution of stochastic differential equations
S. Mauthner · 1998
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The optimal discretization of stochastic differential equations
N. Hofmann, T. Müller-Gronbach, and K. Ritter · 2001
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Strong convergence of Euler-type methods for nonlinear stochastic differential equations
D.J. Higham, X. Mao, and A.M. Stuart · 2002
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An adaptive timestepping algorithm for stochastic differential equations
H. Lamba · 2003
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Optimal pointwise approximation of SDEs based on Brownian motion at discrete points
T. Müller-Gronbach · 2004
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Numerical integration of stochastic differential equations with nonglobally Lipschitz coefficients
G.N. Milstein and M.V. Tretyakov · 2005
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Existence of global weak solutions to some regularized kinetic models for dilute polymers
J.W. Barrett and E. Süli · 2007
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An adaptive Euler-Maruyama scheme for SDEs: convergence and stability
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Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients
The tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients
X. Wang and S. Gan · 2013
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Multilevel Monte Carlo methods
M.B. Giles · 2015
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Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
M. Hutzenthaler and A. Jentzen · 2015
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The truncated Euler-Maruyama method for stochastic differential equations
X. Mao · 2015
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Non-nested adaptive timesteps in multilevel Monte Carlo computations
M.B. Giles, C. Lester, and J. Whittle · 2016
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Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations
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M. Hutzenthaler, A. Jentzen, and P.E. Kloeden · 2011
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Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
M. Hutzenthaler, A. Jentzen, and P.E. Kloeden · 2012
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Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients
X. Mao and L. Szpruch · 2013
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M. Hutzenthaler, A. Jentzen, and X. Wang · 2016
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Convergence rates of the truncated Euler-Maruyama method for stochastic differential equations
X. Mao · 2016
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