Numerical solutions of stochastic differential delay equations under local Lipschitz condition
Journal of Computational and Applied Mathematics
Mathematics and Computers in Simulation
Stochastic differential algebraic equations of index 1 and applications in circuit simulation
Journal of Computational and Applied Mathematics
On weak approximations of (a, b)-invariant diffusions
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems
Journal of Computational and Applied Mathematics
SDELab: A package for solving stochastic differential equations in MATLAB
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
A splitting-step algorithm for reflected stochastic differential equations in R+1
Computers & Mathematics with Applications
The split-step backward Euler method for linear stochastic delay differential equations
Journal of Computational and Applied Mathematics
Split-step backward balanced Milstein methods for stiff stochastic systems
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Split-step forward methods for stochastic differential equations
Journal of Computational and Applied Mathematics
Convergence and stability of the split-step θ-method for stochastic differential equations
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Improved rectangular method on stochastic Volterra equations
Journal of Computational and Applied Mathematics
Physically consistent simulation of mesoscale chemical kinetics: The non-negative FIS-α method
Journal of Computational Physics
Numerical Approximations to the Stationary Solutions of Stochastic Differential Equations
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
A patch that imparts unconditional stability to explicit integrators for Langevin-like equations
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Predictor-corrector methods for a linear stochastic oscillator with additive noise
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
Finite Element Approximation of the Cahn-Hilliard-Cook Equation
SIAM Journal on Numerical Analysis
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Split-step θ-method for stochastic delay differential equations
Applied Numerical Mathematics
An Efficient Semi-Analytical Simulation for the Heston Model
Computational Economics
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Traditional finite-time convergence theory for numerical methods applied to stochastic differential equations (SDEs) requires a global Lipschitz assumption on the drift and diffusion coefficients. In practice, many important SDE models satisfy only a local Lipschitz property and, since Brownian paths can make arbitrarily large excursions, the global Lipschitz-based theory is not directly relevant. In this work we prove strong convergence results under less restrictive conditions. First, we give a convergence result for Euler--Maruyama requiring only that the SDE is locally Lipschitz and that the pth moments of the exact and numerical solution are bounded for some p 2. As an application of this general theory we show that an implicit variant of Euler--Maruyama converges if the diffusion coefficient is globally Lipschitz, but the drift coefficient satisfies only a one-sided Lipschitz condition; this is achieved by showing that the implicit method has bounded moments and may be viewed as an Euler--Maruyama approximation to a perturbed SDE of the same form. Second, we show that the optimal rate of convergence can be recovered if the drift coefficient is also assumed to behave like a polynomial.