The ODE Method and Spectral Theory of Markov Operators
| dc.creator | Huang, J. | |
| dc.creator | Kontoyiannis, I. | |
| dc.creator | Meyn, S. P. | |
| dc.date | 2002-09-20 | |
| dc.date.accessioned | 2026-07-07T04:51:05Z | |
| dc.date.available | 2026-07-07T04:51:05Z | |
| dc.description | We give a development of the ODE method for the analysis of recursive algorithms described by a stochastic recursion. With variability modelled via an underlying Markov process, and under general assumptions, the following results are obtained: 1. Stability of an associated ODE implies that the stochastic recursion is stable in a strong sense when a gain parameter is small. 2. The range of gain-values is quantified through a spectral analysis of an associated linear operator, providing a non-local theory. 3. A second-order analysis shows precisely how variability leads to sensitivity of the algorithm with respect to the gain parameter. All results are obtained within the natural operator-theoretic framework of geometrically ergodic Markov processes. | |
| dc.description | 19 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/math/0209277 | |
| dc.identifier | http://arxiv.org/abs/math/0209277 | |
| dc.identifier | Proceedings of Stochastic Theory and Control Workshop, Springer, New York, pp. 205-221, B. Pasik-Duncan (Editor), 2002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65023 | |
| dc.subject | Probability | |
| dc.subject | Dynamical Systems | |
| dc.title | The ODE Method and Spectral Theory of Markov Operators | |
| dc.type | text |