Most likely paths to error when estimating the mean of a reflected random walk

Duffy, Ken R. and Meyn, Sean P. (2010) Most likely paths to error when estimating the mean of a reflected random walk. Performance Evaluation. ISSN 0166-5316

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It is known that simulation of the mean position of a Reflected Random Walk (RRW) {Wn} exhibits non-standard behavior, even for light-tailed increment distributions with negative drift. The Large Deviation Principle (LDP) holds for deviations below the mean, but for deviations at the usual speed above the mean the rate function is null. This paper takes a deeper look at this phenomenon. Conditional on a large sample mean, a complete sample path LDP analysis is obtained. Let I denote the rate function for the one dimensional increment process. If I is coercive, then given a large simulated mean position, under general conditions our results imply that the most likely asymptotic behavior, ∗, of the paths n−1W⌊tn⌋ is to be zero apart from on an interval [T0, T1] ⊂ [0, 1] and to satisfy the functional equation ∇I

Item Type: Article
Keywords: reflected random walks; queue-length; waiting time; simulation mean position; large deviations; most likely paths;
Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID: 2160
Depositing User: Dr Ken Duffy
Date Deposited: 07 Oct 2010 15:34
Journal or Publication Title: Performance Evaluation
Publisher: Elsevier SD North Holland
Refereed: No

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