EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 28 (2024) ESAIM: PS, 28 (2024) 329-349 References
Open Access
Issue
ESAIM: PS
Volume 28, 2024
Page(s) 329 - 349
DOI https://doi.org/10.1051/ps/2024009
Published online 15 November 2024
  1. A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications. Vol. 38 of Stochastic Modelling and Applied Probability. Springer-Verlag, Berlin (2010). [Google Scholar]
  2. S.R.S. Varadhan, Large deviations and applications. Vol. 46 of CBMS-NSF Regional Conference Series in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1984). [Google Scholar]
  3. T. Rolski, H. Schmidli, V. Schmidt and J. Teugels, Stochastic Processes for Insurance and Finance. Wiley Series in Probability and Statistics. John Wiley & Sons, Ltd., Chichester (1999). [CrossRef] [Google Scholar]
  4. P. Eichelsbacher and M. Löwe, Lindeberg’s method for moderate deviations and random summation. J. Theoret. Probab. 32 (2019) 872–897. [CrossRef] [MathSciNet] [Google Scholar]
  5. H. Mita, Probabilities of large deviations for sums of random number of i.i.d. random variables and its application to a compound Poisson process. Tokyo J. Math. 20 (1997) 353–364. [CrossRef] [MathSciNet] [Google Scholar]
  6. H. Döring and P. Eichelsbacher, Moderate deviations via cumulants. J. Theoret. Probab. 26 (2013) 360–385. [CrossRef] [MathSciNet] [Google Scholar]
  7. B.V. Gnedenko and V.Y. Korolev, Random Summation. CRC Press, Boca Raton, FL (1996). [Google Scholar]
  8. J. Prochno, The large and moderate deviations approach in geometric functional analysis. Preprint arXiv:2403.03940 (2024). [Google Scholar]
  9. A. de Acosta, Upper bounds for large deviations of dependent random vectors. Z. Wahrsch. Verw. Gebiete 69 (1985) 551–565. [CrossRef] [MathSciNet] [Google Scholar]
  10. A. de Acosta, Moderate deviations and associated Laplace approximations for sums of independent random vectors. Trans. Am. Math. Soc. 329 (1992) 357–375. [CrossRef] [Google Scholar]
  11. P. Billingsley, Convergence of Probability Measures. John Wiley & Sons, Inc., New York–London–Sydney (1968). [Google Scholar]
  12. C.R. Baker and I.W. McKeague, Compact covariance operators. Proc. Am. Math. Soc. 83 (1981) 590–593. [CrossRef] [Google Scholar]
  13. J. Lynch and J. Sethuraman, Large deviations for processes with independent increments. Ann. Probab. 15 (1987) 610–627. [CrossRef] [MathSciNet] [Google Scholar]
  14. R.T. Rockafellar, Convex Analysis. Princeton Landmarks in Mathematics. Princeton University Press, Princeton, NJ (1997). [Google Scholar]
  15. E. Schechter, Handbook of Analysis and its Foundations. Academic Press, Inc., San Diego, CA (1997). [Google Scholar]
  16. L. Narici and E. Beckenstein, Topological vector spaces. Vol. 296 of Pure and Applied Mathematics, 2nd edn. CRC Press, Boca Raton, FL (2011). [Google Scholar]
  17. L. Beghin and C. Macci, Large deviations for fractional Poisson processes. Statist. Probab. Lett. 83 (2013) 1193–1202. [CrossRef] [MathSciNet] [Google Scholar]
  18. L. Beghin and E. Orsingher, Fractional Poisson processes and related planar random motions. Electron. J. Probab. 14 (2009) 1790–1827. [CrossRef] [MathSciNet] [Google Scholar]
  19. R. Gorenflo, A.A. Kilbas, F. Mainardi and S.V. Rogosin, Mittag-Leffler Functions, Related Topics and Applications. Springer Monographs in Mathematics. Springer, Heidelberg (2014). [CrossRef] [Google Scholar]
  20. L. Beghin and C. Macci, Asymptotic results for a multivariate version of the alternative fractional Poisson process. Statist. Probab. Lett. 129 (2017) 260–268. [CrossRef] [MathSciNet] [Google Scholar]
  21. R. Giuliano, C. Macci and B. Pacchiarotti, Asymptotic results for runs and empirical cumulative entropies. J. Statist. Plann. Inference 157/158 (2015) 77–89. [CrossRef] [Google Scholar]
  22. P.W. Glynn and W. Whitt, Large deviations behavior of counting processes and their inverses. Queueing Syst. Theory Appl. 17 (1994) 107–128. [CrossRef] [Google Scholar]
  23. P. Billingsley, Probability and Measure. Wiley Series in Probability and Mathematical Statistics, 3rd edn. John Wiley & Sons, Inc., New York (1995). [Google Scholar]
  24. J. Hoffmann-Jørgensen and G. Pisier, The law of large numbers and the central limit theorem in Banach spaces. Ann. Probab. 4 (1976) 587–599. [Google Scholar]
  25. A. de Acosta, On large deviations of sums of independent random vectors, in Probability in Banach spaces, V (Medford, Mass., 1984). Vol. 1153 of Lecture Notes in Math.. Springer, Berlin (1985) 1–14. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.