Hypercontractivity and Its Applications for Functional SDEs of Neutral Type

In this paper, we discuss hypercontractivity for the Markov semigroup $P_t$ which is generated by segment processes associated with a range of functional SDEs of neutral type. As applications, we also reveal that the semigroup $P_t$ converges exponentially to its unique invariant probability measure $μ$ in entropy, $L^2 (μ)$ and $\|\cdot\|_{\mbox{var}}$, respectively.

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