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Stability and Decay Rate of the Numerical Approximation for Neutral Stochastic Functional Differential Equations

Rong Hu

Abstract


This work examines the exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations (NSFDEs). We firstly establish the moment exponential stability criterion of the numerical solution. Then we examine the conditions under which the numerical solution can reproduce the exponential mean square stability of the exact solution. It is shown that the numerical solution not only share the exponential mean square stability of the exact solution, but also preserve the decay rate as measured by the bound of the Lyapunov exponent.

Keywords


Neutral stochastic functional differential equations, Exponential stability, Euler-Maruyama method.

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