Some experiments on numerical simulations of stochastic differential equations and a new algorithm
Journal of Computational Physics
Stability Analysis of Numerical Schemes for Stochastic Differential Equations
SIAM Journal on Numerical Analysis
Ergodic Control of Switching Diffusions
SIAM Journal on Control and Optimization
Balanced Implicit Methods for Stiff Stochastic Systems
SIAM Journal on Numerical Analysis
Mean-Square and Asymptotic Stability of the Stochastic Theta Method
SIAM Journal on Numerical Analysis
Mathematics and Computers in Simulation
Option Pricing With Markov-Modulated Dynamics
SIAM Journal on Control and Optimization
Strong approximations of stochastic differential equations with jumps
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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In this paper numerical methods for solving stochastic differential equations with Markovian switching (SDEwMSs) are developed by pathwise approximation. The proposed family of strong predictor-corrector Euler-Maruyama methods is designed to overcome the propagation of errors during the simulation of an approximate path. This paper not only shows the strong convergence of the numerical solution to the exact solution but also reveals the order of the error under some conditions on the coefficient functions. A natural analogue of the p-stability criterion is studied. Numerical examples are given to illustrate the computational efficiency of the new predictor-corrector Euler-Maruyama approximation.