Approximation of upper Lyapunov exponents of bilinear stochastic differential systems
SIAM Journal on Numerical Analysis
Journal of Optimization Theory and Applications
Strong discrete time approximation of stochastic differential equations with time delay
Mathematics and Computers in Simulation
Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
SIAM Journal on Numerical Analysis
Convergence of numerical solutions to stochastic age-dependent population equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Numerical solutions for a class of nonlinear systems and application to stochastic resonance
WSEAS Transactions on Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
A stochastic minimum principle and an adaptive pathwise algorithm for stochastic optimal control
Automatica (Journal of IFAC)
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Stochastic differential equations with Markovian switching (SDEwMSs), one of the important classes of hybrid systems, have been used to model many physical systems that are subject to frequent unpredictable structural changes. The research in this area has been both theoretical and applied. Most of SDEwMSs do not have explicit solutions so it is important to have numerical solutions. It is surprising that there are not any numerical methods established for SDEwMSs yet, although the numerical methods for stochastic differential equations (SDEs) have been well studied. The main aim of this paper is to develop a numerical scheme for SDEwMSs and estimate the error between the numerical and exact solutions. This is the first paper in this direction and the emphasis lies on the error analysis.