an:06849906
Zbl 1390.60241
Li, Zhi; Yan, Litan; Zhou, Xianghui
Global attracting sets and stability of neutral stochastic functional differential equations driven by Rosenblatt process
EN
Front. Math. China 13, No. 1, 87-105 (2018).
00374647
2018
j
60H15
global attracting sets; exponential \(p\)-th moment stability; Rosenblatt process
Summary: We are concerned with a class of neutral stochastic partial differential equations driven by Rosenblatt process in a Hilbert space. By combining some stochastic analysis techniques, tools from semigroup theory, and stochastic integral inequalities, we identify the global attracting sets of this kind of equations. Especially, some sufficient conditions ensuring the exponent \(p\)-stability of mild solutions to the stochastic systems under investigation are obtained. Last, an example is given to illustrate the theory in the work.