Abstract
The main aim of this work is to establish an averaging principle for a wide
class of interacting particle systems in the continuum.
This principle is an important step in the analysis of Markov evolutions and is
usually applied for the associated semigroups related to backward Kolmogorov
equations, c.f. [27].
Our approach is based on the study of forward Kolmogorov equations (a.k.a.
Fokker-Planck equations).
We describe a system evolving as a Markov process on the space of finite
configurations, whereas its rates depend on the actual state of another
(equilibrium) process
on the space of locally finite configurations. We will show that ergodicity of
the environment process implies the averaging principle for the solutions of
the
coupled Fokker-Planck equations.
Key words: Averaging principle, Fokker-Planck equation, interacting particle systems,
weak-coupling, random evolution.
Full Text
Article Information
| Title | Weak-coupling limit for ergodic environments |
| Source | Methods Funct. Anal. Topology, Vol. 25 (2019), no. 2, 118-133 |
| MathSciNet |
MR3978676 |
| Milestones | Received 31/07/2018; Revised 22/01/2019 |
| Copyright | The Author(s) 2019 (CC BY-SA) |
Authors Information
Martin Friesen
Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany
Yuri Kondratiev
Department of Mathematics, Bielefeld University, Germany
Citation Example
Martin Friesen and Yuri Kondratiev, Weak-coupling limit for ergodic environments, Methods Funct. Anal. Topology 25
(2019), no. 2, 118-133.
BibTex
@article {MFAT1167,
AUTHOR = {Martin Friesen and Yuri Kondratiev},
TITLE = {Weak-coupling limit for ergodic environments},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {25},
YEAR = {2019},
NUMBER = {2},
PAGES = {118-133},
ISSN = {1029-3531},
MRNUMBER = {MR3978676},
URL = {http://mfat.imath.kiev.ua/article/?id=1167},
}
