Hypercontractivity and Its Applications for Functional SDEs of Neutral Type

Jianhai Bao, Chenggui Yuan

Published 2015-01-25Version 1

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 $\mu$ in entropy, $L^2 (\mu)$ and $\|\cdot\|_{\mbox{var}}$, respectively.