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- W4366604961 abstract "The aim of this paper is to get asymptotic deviation bounds via a Large Deviation Principle (LDP) for cumulative processes also known as compound renewal processes or renewal-reward processes. These processes cumulate independent random variables occurring in time interval given by a renewal process. Our result extends the one obtained in Lefevere et al. (2011) in the sense that we impose no specific dependency between the cumulated random variables and the renewal process and the proof uses Mariani et al. (2014). In the companion paper Cattiaux-Costa-Colombani (2021) we apply this principle to Hawkes processes with inhibition. Under some assumptions Hawkes processes are indeed cumulative processes, but they do not enter the framework of Lefevere et al. (2011)." @default.
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- W4366604961 date "2023-09-01" @default.
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- W4366604961 title "Asymptotic deviation bounds for cumulative processes" @default.
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- W4366604961 doi "https://doi.org/10.1016/j.spa.2023.05.010" @default.
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