The General Stability Of Time-Changed Stochastic Differential Equations

In recent years,because of the effective applications of stochastic differential equations in practical problem,stability analysis about stochastic differential equations has been became more important.Compared with traditional stochastic differential equations driven by Brownian motion,stochastic differential equations with time-changed processes are more realistic and closely related to fractional-order differential equations.We first use the It(?) formula for time-changed processes time-changed to obtain the moment stability of the equation in the general sense of decay rate.Next,using the law of large numbers,we establish the general almost surely stability of timechanged stochastic differential equations under more general conditions.Then,we define a stopping time and use it to prove a comparison principle.Finally,the abstract results are illustrated by computer simulations.