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Duffy, Ken R. and Metcalfe, Anthony P. (2005) How to estimate a cumulative process’s rate-function. Journal of Applied Probability, 42 (4). pp. 1044-1052. ISSN 0021-9002
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Abstract
Consider two sequences of bounded random variables, a value and a timing process, that satisfy the large deviation principle (LDP) with rate-function J(·,·) and whose cumulative process satisfies the LDP with rate-function I(·). Under mixing conditions, an LDP for estimates of I
constructed by transforming an estimate of J is proved. For the case of cumulative renewal processes it is demonstrated that this approach is favorable to a more direct method as it ensures the laws of the estimates converge weakly to a Dirac measure at I.
| Item Type: | Article |
|---|---|
| Keywords: | Estimating large deviations; Cumulative process; Renewal process; Hamilton Institute. |
| Academic Unit: | Faculty of Science and Engineering > Research Institutes > Hamilton Institute Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: | 1844 |
| Depositing User: | Hamilton Editor |
| Date Deposited: | 15 Feb 2010 15:38 |
| Journal or Publication Title: | Journal of Applied Probability |
| Publisher: | Applied Probability Trust |
| Refereed: | Yes |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/1844 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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