Ergodicity and Stationary Solution for Stochastic Neutral Retarded Partial Differential Equations Driven by Fractional Brownian Motion

Zhi Li () and Litan Yan ()
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Zhi Li: Yangtze University
Litan Yan: Donghua University

Journal of Theoretical Probability, 2019, vol. 32, issue 3, 1399-1419

Abstract: Abstract 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 $$C_0$$ 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.

Keywords: Fractional Brownian motion; Stochastic functional equation of neutral type; Stationary solution; Erodicity; 60H15; 60G15; 60H05 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-018-0810-8

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