Basis Markov Partitions and Transition Matrices for Stochastic Systems
| dc.creator | Bollt, Erik | |
| dc.creator | Gora, Pawel | |
| dc.creator | Ostruszka, Andrzej | |
| dc.creator | Zyczkowski, Karol | |
| dc.date | 2006-05-08 | |
| dc.date.accessioned | 2026-07-07T07:14:48Z | |
| dc.date.available | 2026-07-07T07:14:48Z | |
| dc.description | We analyze dynamical systems subjected to an additive noise and their deterministic limit. In this work, we will introduce a notion by which a stochastic system has something like a Markov partition for deterministic systems. For a chosen class of the noise profiles the Frobenius-Perron operator associated to the noisy system is exactly represented by a stochastic transition matrix of a finite size K. This feature allows us to introduce for these stochastic systems a basis--Markov partition, defined herein, irrespectively of whether the deterministic system possesses a Markov partition or not. We show that in the deterministic limit, corresponding to K --> infinity, the sequence of invariant measures of the noisy systems tends, in the weak sense, to the invariant measure of the deterministic system. Thus by introducing a small additive noise one may approximate transition matrices and invariant measures of deterministic dynamical systems. | |
| dc.description | 21 pages in latex including 3 figures | |
| dc.identifier | https://arxiv.org/abs/nlin/0605017 | |
| dc.identifier | http://arxiv.org/abs/nlin/0605017 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/113028 | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Basis Markov Partitions and Transition Matrices for Stochastic Systems | |
| dc.type | text |