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LARGE DEVIATION PRINCIPLES FOR CUMULATIVE PROCESSES AND APPLICATIONS

Abstract : The aim of this paper is to prove a Large Deviation Principle (LDP) for cumulative processes also known as coumpound renewal processes. These processes cumulate independent random variables occuring in time interval given by a renewal process. Our result extends the one obtained in Lefevère et al. [13] in the sense that we impose no specific dependency between the cumulated random variables and the renewal process. The proof is inspired from [13] but deals with additional difficulties due to the general framework that is considered here. In the companion paper Cattiaux et al. [6] 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 [13].
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https://hal.archives-ouvertes.fr/hal-03344425
Contributor : Manon Costa Connect in order to contact the contributor
Submitted on : Wednesday, September 15, 2021 - 8:57:20 AM
Last modification on : Tuesday, October 19, 2021 - 11:17:07 PM

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  • HAL Id : hal-03344425, version 1

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Patrick Cattiaux, Laetitia Colombani, Manon Costa. LARGE DEVIATION PRINCIPLES FOR CUMULATIVE PROCESSES AND APPLICATIONS. 2021. ⟨hal-03344425⟩

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