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Large deviations for vector-valued Lévy processes

Author

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  • de Acosta, A.

Abstract

The large deviation principle is proved for the rescaled and normalized paths of a Lévy process taking values in a separable Banach space B, in the uniform topology of D([0, 1], B), under an exponential integrability condition. Other results are obtained when this condition does not hold.

Suggested Citation

  • de Acosta, A., 1994. "Large deviations for vector-valued Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 51(1), pages 75-115, June.
    • Handle: RePEc:eee:spapps:v:51:y:1994:i:1:p:75-115
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    Cited by:

    1. Macci, Claudio & Pacchiarotti, Barbara, 2015. "Large deviations for a class of counting processes and some statistical applications," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 36-48.
    2. Jiang, Tiefeng & Rao, M. Bhaskara & Wang, Xiangchen, 1995. "Large deviations for moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 309-320, October.
    3. Léonard, C., 2000. "Large deviations for Poisson random measures and processes with independent increments," Stochastic Processes and their Applications, Elsevier, vol. 85(1), pages 93-121, January.
    4. Michel Mandjes, 2022. "Multivariate M/G/1 systems with coupled input and parallel service," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 309-311, April.
    5. Budhiraja, Amarjit & Chen, Jiang & Dupuis, Paul, 2013. "Large deviations for stochastic partial differential equations driven by a Poisson random measure," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 523-560.
    6. Jorge Garcia, 2008. "A Large Deviation Principle for Stochastic Integrals," Journal of Theoretical Probability, Springer, vol. 21(2), pages 476-501, June.
    7. Dembo, Amir & Zajic, Tim, 1995. "Large deviations: From empirical mean and measure to partial sums process," Stochastic Processes and their Applications, Elsevier, vol. 57(2), pages 191-224, June.
    8. Macci, Claudio & Torrisi, Giovanni Luca, 2011. "Risk processes with shot noise Cox claim number process and reserve dependent premium rate," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 134-145, January.
    9. Adrien Genin & Peter Tankov, 2016. "Optimal importance sampling for L\'evy Processes," Papers 1608.04621, arXiv.org.
    10. Macci, Claudio, 2008. "Large deviations for the time-integrated negative parts of some processes," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 75-83, January.
    11. Asmussen, Søren & Fuckerieder, Pascal & Jobmann, Manfred & Schwefel, Hans-Peter, 2002. "Large deviations and fast simulation in the presence of boundaries," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 1-23, November.
    12. Djellout, Hacène & Guillin, Arnaud & Samoura, Yacouba, 2017. "Estimation of the realized (co-)volatility vector: Large deviations approach," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2926-2960.
    13. Yongzhao Shao & Raúl Jiménez, 1998. "Entropy for Random Partitions and Its Applications," Journal of Theoretical Probability, Springer, vol. 11(2), pages 417-433, April.
    14. Daras, Tryfon, 1998. "Trajectories of exchangeable sequences: Large and moderate deviations results," Statistics & Probability Letters, Elsevier, vol. 39(4), pages 289-304, August.
    15. Florens, Danielle & Pham, Huyên, 1998. "Large deviation probabilities in estimation of Poisson random measures," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 117-139, August.

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