Stability of Stochastic Functional Differential Equations with Switching

To study the stability of a class of stochastic functional differential equations with continuous dynamics and concomitant discrete events, the mean square exponential stability was studied based on \mathrmIt\hat \mathrmo formula for the exact solution of the stochastic functional differential equations with Markov switching. And the mean square exponential stability was also studied based on Euler-Maruyama method for the numerical solution of the equation. In addition, some numerical examples and simulations were carried out to verify the exponential stability of the exact and numerical solutions of the equation.