On absolute continuity of invariant measures associated with a piecewise-deterministic Markov process with random switching between flows
Authors:
- Dawid Czapla,
- Katarzyna Horbacz,
- Hanna Wojewódka-Ściążko
Abstract
We are concerned with the absolute continuity of stationary distributions corresponding to some piecewise deterministic Markov process, being typically encountered in biological models. The process under investigation involves a deterministic motion punctuated by random jumps, occurring at the jump times of a Poisson process. The post-jump locations are obtained via random transformations of the pre-jump states. Between the jumps, the motion is governed by continuous semiflows, which are switched directly after the jumps. The main goal of this paper is to provide a set of verifiable conditions implying that any invariant distribution of the process under consideration that corresponds to an ergodic invariant measure of the Markov chain given by its post-jump locations has a density with respect to the Lebesgue measure.
- Record ID
- USL6575f95f75ee4ae69400576e88865224
- Author
- Journal series
- Nonlinear Analysis-Theory Methods & Applications, ISSN 0362-546X, e-ISSN 1873-5215
- Issue year
- 2021
- Vol
- 213
- Pages
- 1-26
- Publication size in sheets
- 1.30
- Article number
- 112522
- Keywords in English
- Piecewise-deterministic Markov process; Invariant measure; Ergodic measure; Absolute continuity; Singularity; Switching semiflows
- ASJC Classification
- ;
- DOI
- DOI:10.1016/j.na.2021.112522 Opening in a new tab
- Handle.net URL
- hdl.handle.net/20.500.12128/21045 Opening in a new tab
- URL
- https://www.sciencedirect.com/science/article/pii/S0362546X21001759?via%3Dihub Opening in a new tab
- Language
- eng (en) English
- License
- File
-
- File: 1
- On absolute continuity of invariant measures associated with a piecewise-deterministic Markov process with random switching between flows, File Czapla_On_absolute_continuity.pdf / 1 MB
- Czapla_On_absolute_continuity.pdf
- publication date: 06-02-2024
- On absolute continuity of invariant measures associated with a piecewise-deterministic Markov process with random switching between flows, File Czapla_On_absolute_continuity.pdf / 1 MB
-
- Score (nominal)
- 140
- Score source
- journalList
- Score
- = 140.0, 07-07-2023, ArticleFromJournal
- Publication indicators
- Uniform Resource Identifier
- https://opus.us.edu.pl/info/article/USL6575f95f75ee4ae69400576e88865224/
- URN
urn:uni-kat-prod:USL6575f95f75ee4ae69400576e88865224
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