Exponential stability for some stochastic neutral partial functional integrodifferential equations with delays and Poisson jumps
The paper deals with stochastic neutral partial functional integro-differential equations with delays in a real separable Hilbert space. The noise term is represented by a Wiener process and Poisson jumps. The main result of the paper, Theorem 3.1, gives sufficient conditions for the existence and exponential stability in the mean square sense of mild solutions to the equations under consideration. The main result is proved under the assumption that the linear part of the equations has a resolvent operator. The proof of the result is given in details. It is based on the Banach fixed point principle. The paper seems to be an interesting contribution to current stability theory of stochastic equations. Moreover, in the paper an application of the results obtained is provided. The references cited in the paper are representative enough for the problem studied.
neutral partial functional integro-differential equations
exponential stability in the mean square sense
scientific article; zbMATH DE number 6343958