Hypercontractivity and Its Applications for Functional SDEs of Neutral Type
arXiv:1501.06186
Abstract
In this paper, we discuss hypercontractivity for the Markov semigroup which is generated by segment processes associated with a range of functional SDEs of neutral type. As applications, we also reveal that the semigroup converges exponentially to its unique invariant probability measure in entropy, and $\|\cdot\|_{\mbox{var}}$, respectively.
14 pages