Exponential mean square stability of numerical methods for systems of stochastic differential equations
Copyright policy )Exponential mean square stability of numerical methods for systems of stochastic differential equations
A theorem is proved that establishes numerical exponential mean square stability (NEMSS) of the classic theta method and the split-step theta method for systems of linear Itô stochastic differential equations (SDEs) that are exponentially mean square stable. Then theorems are proved giving conditions that imply that split-step theta methods for nonlinear systems of SDEs have NEMSS and conditions that imply that they do not. The paper concludes with extension of these results to systems of SDEs with Poisson-driven jumps.
- Huazhong University of Science and Technology China (People's Republic of)
Numerical solutions to stochastic differential and integral equations, mean square stability, Mean square stability, Ordinary differential equations and systems with randomness, exponential stability, Applied Mathematics, Poisson process, Theta method, Exponential stability, Stochastic ordinary differential equations (aspects of stochastic analysis), Computational Mathematics, Stochastic differential equations, theta method, Stability and convergence of numerical methods for ordinary differential equations, systems of linear Itô stochastic differential equations, Computational methods for stochastic equations (aspects of stochastic analysis)
Numerical solutions to stochastic differential and integral equations, mean square stability, Mean square stability, Ordinary differential equations and systems with randomness, exponential stability, Applied Mathematics, Poisson process, Theta method, Exponential stability, Stochastic ordinary differential equations (aspects of stochastic analysis), Computational Mathematics, Stochastic differential equations, theta method, Stability and convergence of numerical methods for ordinary differential equations, systems of linear Itô stochastic differential equations, Computational methods for stochastic equations (aspects of stochastic analysis)
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