Mean-square stability properties of an adaptive time-stepping SDE solver
Journal of Computational and Applied Mathematics
On weak approximations of (a, b)-invariant diffusions
Mathematics and Computers in Simulation
On mean-square stability properties of a new adaptive stochastic Runge-Kutta method
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Split-step backward balanced Milstein methods for stiff stochastic systems
Applied Numerical Mathematics
Split-step forward methods for stochastic differential equations
Journal of Computational and Applied Mathematics
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In this paper we describe a general 2nd-order accurate (weak sense) procedure for stabilizing Monte-Carlo simulations of Itô stochastic differential equations. The splitting procedure includes explicit Runge--Kutta (Heun) methods, semi-implicit methods, and the trapezoidal rule. We prove the semi-implicit method of Öttinger [Stochastic Processes in Polymeric Fluids, Springer-Verlag, Berlin, 1996] for stabilizing simulations in the presence of nonlinear drift coefficients.