Kirchner, Matthias; Torrisi, Giovanni Luca (2026). Nonlinear Marked Poisson Autoregression: Stability and Rate of Convergence to Equilibrium. Journal of Theoretical Probability, 39 (18). 10.1007/s10959-025-01475-0
![[img]](https://phrepo.phbern.ch/style/images/fileicons/text.png) |
Text
s10959-025-01475-0.pdf - Published Version Restricted to registered users only Available under License Publisher holds Copyright. Download (518kB) | Request a copy |
We consider nonlinear marked Poisson autoregressions and we prove the existence and uniqueness (in law) of the ergodic version under various assumptions on the transfer function, the coefficient functions, and the mark distribution. Moreover, by means of coupling techniques we discuss the convergence and the rate of convergence to equilibrium of a non-ergodic version of the time series, starting from some “initial condition”, to the ergodic version. The theoretical results are illustrated by examples and numerical simulations.
Item Type: |
Journal Article (Original Article) |
|---|---|
PHBern Contributor: |
Kirchner, Matthias |
ISSN: |
1572-9230 |
Language: |
English |
Submitter: |
Matthias Kirchner |
Date Deposited: |
23 Jan 2026 16:20 |
Last Modified: |
24 Jan 2026 11:05 |
Publisher DOI: |
10.1007/s10959-025-01475-0 |
Uncontrolled Keywords: |
Nonlinear time series, Nonlinear autoregression, Ergodic processes, Rate of convergence to equilibrium |
PHBern DOI: |
10.57694/7956 |
URI: |
https://phrepo.phbern.ch/id/eprint/7956 |
Actions (login required)
 |
Edit item |