Markov semigroups with hypocoercive-type generator in infinite dimensions: Ergodicity and smoothing

Michela Ottobre, Boguslaw Zegarlinski, Vasilis Kontis

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5 Citations (Scopus)

Abstract

We start by considering finite dimensional Markovian dynamics in Rm generated by operators of hypocoercive type and for such models we obtain short and long time pointwise estimates for all the derivatives, of any order and in any direction, along the semigroup. We then look at infinite dimensional models (in (Rm)Zd) produced by the interaction of infinitely many finite dimensional dissipative dynamics of the type indicated above. For these infinite dimensional models we study finite speed of propagation of information, well-posedness of the semigroup, time behaviour of the derivatives and strong ergodicity problem.
Original languageEnglish
Pages (from-to)3173-3223
Number of pages51
JournalJournal of Functional Analysis
Volume270
Issue number9
Early online date7 Mar 2016
DOIs
Publication statusPublished - 1 May 2016

Keywords

  • Hypocoercivity
  • Ergodic theory
  • Degenerate diffusions
  • Infinite dimensional Markov semigroup

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