Stability Analysis Of Two Class Of Stochastic Differential Equations With Delays

This thesis is concerned with exponential stability of energy solutions to astochastic diferential equations with jumps and delays, and stability of a class of impulsivestochastic diferential equation with mixed time delays, respectively.In Chapter2, the exponential stability of energy solutions to a class of stochasticdiferential equations with jumps and delays was studied. By the estimate of the coefcientsfunctions in the stochastic energy equality, some sufcient conditions for exponential stabilityand almost sure exponential stability of energy solutions were obtained.In Chapter3, a class of impulsive stochastic diferential equation with mixed time delayswas considered. First, an impulsive control for a stochastic delay diferential equations wasconstructed. Then, the equivalent relation between the solution of impulsive stochastic dif-ferential equations with mixed time delays and that of a corresponding stochastic diferentialequations with mixed time delays was established, some sufcient conditions of stability ofequilibrium point were established.