Large deviations with diminishing rates

• 成果类型: Article
• 署名作者: Shwartz, A; Weiss, A
• 署名单位: Technion Israel Institute of Technology; AT&T; Alcatel-Lucent; Lucent Technologies
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1040.0121
• 发表日期: 2005
• 页码: 281-310
• 关键词: large number; overflow

摘要

The theory of large deviations for jump Markov processes has been generally proved only when jump rates are bounded below, away from zero (Dupuis and Ellis, 1995, The large deviations principle for a general class of queueing systems I. Trans. Amer Moth. Soc. 347 2689-2751; Ignatiouk-Robert, 2002, Sample path large deviations and convergence parameters. Ann. Appl. Probab. 11 1292-1329; Shwartz and Weiss, 1995, Large Deviations for Performance Analysis, Chapman-Hall). Yet, various applications of interest do not satisfy this condition. We describe several classes of models where jump rates diminish to zero in a Lipschitz continuous way. Under appropriate conditions, we prove that the sample path large deviations principle continues to hold. Under our conditions, the rate function remains an integral over a local rate function, which retains its standard representation.