Malyk I. Stability of the stochastic dynamical system of neutral type with aftereffect

The thesis is devoted to the investigation of asymptotic behavior of the solution of stochastic functional differential equations with finite prehistory. The theorem of existence and uniqueness of the l -moment of strong solution of the stochastic integral differential Volterra’s equation with integral on Poisson measure and proved. The necessary and sufficient conditions of the asymptotic stability in the mean square are obtained for the solution of the linear stochastic differential difference and functional differential systems of neutral type. Abovementioned theoretical results are applied to the analysis of the investor’s behavior on (B, S) -market.