Large deviations for a class of nonhomogeneous Markov chains

• 成果类型: Article
• 署名作者: Dietz, Z; Sethuraman, S
• 署名单位: Tulane University; Iowa State University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000990
• 发表日期: 2005
• 页码: 421-486
• 关键词: low-temperature; metastability; DYNAMICS; limit; entropy; THEOREM

摘要

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, 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, 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 --> P is irregular. Results in the intermediate regime apply to geometrically fast running optimizations, and to some issues in glassy physics.