Some simple but challenging Markov processes
By Florent Malrieu. 2014
55 citations recorded by the source corpus.
In this note, we present few examples of Piecewise Deterministic Markov Processes and their long time behavior. They share two important features: they are related to concrete models (in biology, networks, chemistry,. . .) and they are mathematically rich. Their math-ematical study relies on coupling method, spectral decomposition, PDE technics, functional inequalities. We also relate these simple examples to recent and open problems.
Subfields: Molecular Biology
View Paper: https://www.semanticscholar.org/paper/60649db95d770c65496b0672477d5abc5167573c
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In Molecular Biology
- Pierre-André Zitt
- Arnaud Guillin
- Pierre Monmarch'e
- Joris Bierkens
- Gareth O. Roberts
- Alain Oliviero Durmus
- Jeffrey S. Rosenthal
- Radford M. Neal
Citations in the corpus
- Ergodicity of the zigzag process (2017, background): “As the name suggests, PDMPs follow deterministic dynamics, in between random times where they may jump or change to another deterministic dynamics (see [2, 25] for examples and additional references).”
- Piecewise deterministic Markov processes and their invariant measures (2018, background): “Several examples of PDMP can be found in [18] and references therein.”