Hypercontractivity and Its Applications for Functional SDEs of Neutral Type
Abstract
In this paper, we discuss hypercontractivity for the Markov semigroup Pt which is generated by segment processes associated with a range of functional SDEs of neutral type. As applications, we also reveal that the semigroup Pt converges exponentially to its unique invariant probability measure μ in entropy, L2 (μ) and \|·\|var, respectively.
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