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 01665316
(Submitted)
Abstract
It is known that simulation of the mean position of a Reflected Random Walk (RRW) {Wn}
exhibits nonstandard behavior, even for lighttailed 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; queuelength; 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 
URI: 

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