Hypercontractivity and Its Applications for Functional SDEs of Neutral Type

Jianhai Bao; Chenggui Yuan

Hypercontractivity and Its Applications for Functional SDEs of Neutral Type

Probability 2015-01-27 v1

Authors: Jianhai Bao , Chenggui Yuan

Abstract

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.

Keywords

operator semigroups markov processes topological semigroups

Cite

@article{arxiv.1501.06186,
  title  = {Hypercontractivity and Its Applications for Functional SDEs of Neutral Type},
  author = {Jianhai Bao and Chenggui Yuan},
  journal= {arXiv preprint arXiv:1501.06186},
  year   = {2015}
}

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14 pages

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