Abstract
We discuss the ergodic properties of quasi-Markovian stochastic differential equations, providing general conditions that ensure existence and uniqueness of a smooth invariant distribution and exponential convergence of the evolution operator in suitably weighted L∞ spaces, which implies the validity of central limit theorem for the respective solution processes. The main new result is an ergodicity condition for the generalized Langevin equation with configuration-dependent noise and (non-)conservative force.
Original language | English |
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Title of host publication | Stochastic Dynamics Out of Equilibrium - Institut Henri Poincaré, 2017 |
Editors | Giambattista Giacomin, Stefano Olla, Ellen Saada, Herbert Spohn, Gabriel Stoltz, Gabriel Stoltz |
Publisher | Springer |
Pages | 282-330 |
Number of pages | 49 |
ISBN (Print) | 9783030150952 |
DOIs | |
Publication status | Published - 2019 |
Event | International workshop on Stochastic Dynamics out of Equilibrium, IHPStochDyn 2017 - Paris, France Duration: 12 Jun 2017 → 16 Jun 2017 |
Publication series
Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 282 |
ISSN (Print) | 2194-1009 |
ISSN (Electronic) | 2194-1017 |
Conference
Conference | International workshop on Stochastic Dynamics out of Equilibrium, IHPStochDyn 2017 |
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Country/Territory | France |
City | Paris |
Period | 12/06/17 → 16/06/17 |
Bibliographical note
Funding Information:Acknowledgements. The authors wish to thank Greg Pavliotis (Imperial), Jonathan Mattingly (Duke) and Gabriel Stoltz (ENPC) for their generous assistance in providing comments at various stages of this project. In particular, the authors thank Jonathan Mattingly for pointing out the possibility of using Girsanov’s theorem in the proof of Lemma 7. Both authors acknowledge the support of the European Research Council (Rule Project, grant no. 320823). BJL further acknowledges the support of the EPSRC (grant no. EP/P006175/1) during the preparation of this article. The work of MS was supported by the National Science Foundation under grant DMS-1638521 to the Statistical and Applied Mathematical Sciences Institute.
Publisher Copyright:
© Springer Nature Switzerland AG 2019.
Keywords
- Central limit theorem
- Ergodicity
- Generalized Langevin equation
- Heat-bath
- Molecular dynamics
- Mori-Zwanzig formalism
- Non-equilibrium
- Quasi-Markovian model
- Reduced model
- Sampling
ASJC Scopus subject areas
- General Mathematics