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Ergodicity and stationary solution for stochastic neutral retarded partial differential equations driven by fractional Brownian motion. (English) Zbl 1447.60114
Summary: In this paper, we discuss a class of neutral retarded stochastic functional differential equations driven by a fractional Brownian motion on Hilbert spaces. We develop a $$C_0$$-semigroup theory of the driving deterministic neutral system and formulate the neutral time delay equation under consideration as an infinite-dimensional stochastic system without time lag and neutral item. Consequently, a criterion is presented to identify a strictly stationary solution for the systems considered. In particular, the ergodicity of the strictly stationary solution is studied. Subsequently, the ergodicity behavior of non-stationary solution for the systems considered is also investigated. We present an example which can be explicitly determined to illustrate our theory in the work.
##### MSC:
 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 60G15 Gaussian processes 60H05 Stochastic integrals 60G22 Fractional processes, including fractional Brownian motion
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