How to estimate a cumulative process’s rate-function
Duffy, Ken 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
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.
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