Given a random dynamical system T constructed from Jablonski transformations, consider its Perron-Frobenius operator P_T.
We prove a weak form of the Lasota-Yorke inequality for P_T and
thereby prove the existence of BV- invariant densities for T. Using the Spectral Decomposition Theorem we prove that the support of an invariant density is open a.e. and give conditions
such that the invariant density for T is unique. We study the asymptotic behavior
of the Markov operator P_T, especially when T has a unique absolutely continuous invariant measure (ACIM). Under the assumption of uniqueness, we obtain spectral stability in the sense of Keller. As an application, we can use Ulam's method to approximate the invariant density of P_T.
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/1253 |
| Date | 13 November 2008 |
| Creators | Hsieh, Li-Yu Shelley |
| Contributors | Bose, Chris |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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