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Large deviations for renewal processes

Author

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  • Lefevere, Raphaël
  • Mariani, Mauro
  • Zambotti, Lorenzo

Abstract

We investigate large deviations for the empirical measure of the forward and backward recurrence time processes associated with a classical renewal process with arbitrary waiting-time distribution. The Donsker-Varadhan theory cannot be applied in this case, and indeed it turns out that the large deviations rate functional differs from the one suggested by such a theory. In particular, a non-strictly convex and non-analytic rate functional is obtained.

Suggested Citation

  • Lefevere, Raphaël & Mariani, Mauro & Zambotti, Lorenzo, 2011. "Large deviations for renewal processes," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2243-2271, October.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:10:p:2243-2271
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    Cited by:

    1. Manish Meena & Hrishikesh Kumar & Nitin Dutt Chaturvedi & Andrey A. Kovalev & Vadim Bolshev & Dmitriy A. Kovalev & Prakash Kumar Sarangi & Aakash Chawade & Manish Singh Rajput & Vivekanand Vivekanand , 2023. "Biomass Gasification and Applied Intelligent Retrieval in Modeling," Energies, MDPI, vol. 16(18), pages 1-21, September.
    2. Zamparo, Marco, 2021. "Large deviations in discrete-time renewal theory," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 80-109.
    3. Cattiaux, Patrick & Colombani, Laetitia & Costa, Manon, 2023. "Asymptotic deviation bounds for cumulative processes," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 85-105.
    4. Cattiaux, Patrick & Colombani, Laetitia & Costa, Manon, 2022. "Limit theorems for Hawkes processes including inhibition," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 404-426.
    5. Zamparo, Marco, 2023. "Large deviation principles for renewal–reward processes," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 226-245.

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