Large deviations for a class of nonhomogeneous Markov chains
| dc.creator | Dietz, Zach | |
| dc.creator | Sethuraman, Sunder | |
| dc.date | 2004-04-12 | |
| dc.date | 2005-04-06 | |
| dc.date.accessioned | 2026-07-07T05:07:23Z | |
| dc.date.available | 2026-07-07T05:07:23Z | |
| dc.description | Large deviation results are given for a class of perturbed nonhomogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {P_n} be a sequence of transition matrices on a finite state space which converge to a limit transition matrix P. Let {X_n} be the associated nonhomogeneous Markov chain where P_n controls movement from time n-1 to n. The main statements are a large deviation principle and bounds for additive functionals of the nonhomogeneous process under some regularity conditions. In particular, when P is reducible, three regimes that depend on the decay of certain ``connection'' P_n probabilities are identified. Roughly, if the decay is too slow, too fast or in an intermediate range, the large deviation behavior is trivial, the same as the time-homogeneous chain run with P or nontrivial and involving the decay rates. Examples of anomalous behaviors are also given when the approach P_n\to P is irregular. Results in the intermediate regime apply to geometrically fast running optimizations, and to some issues in glassy physics. | |
| dc.description | Published at http://dx.doi.org/10.1214/105051604000000990 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0404230 | |
| dc.identifier | http://arxiv.org/abs/math/0404230 | |
| dc.identifier | Annals of Applied Probability 2005, Vol. 15, No. 1A, 421-486 | |
| dc.identifier | doi:10.1214/105051604000000990 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70840 | |
| dc.subject | Probability | |
| dc.subject | 60J10 (Primary) 60F10. (Secondary) | |
| dc.title | Large deviations for a class of nonhomogeneous Markov chains | |
| dc.type | text |