Geodesic
Moderately large deviation principles for trajectories of compound renewal processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 2, pp. 399-411 Cet article a éte moissonné depuis la source Math-Net.Ru

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Moderate large deviations principles for trajectories of compound renewal processes are put forward assuming that either the Cramér condition is satisfied or weaker moment conditions are satisfied.
Keywords: compound renewal processes, moderate large deviations principle, crude (logarithmic) invariance principle.
Mots-clés : Cramér condition 
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A. A. Borovkov. Moderately large deviation principles for trajectories of compound renewal processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 2, pp. 399-411. http://geodesic.mathdoc.fr/item/TVP_2019_64_2_a8/

[1] A. A. Borovkov, K. A. Borovkov, Asymptotic analysis of random walks. Heavy-tailed distributions, Encyclopedia Math. Appl., Cambridge Univ. Press, Cambridge, 118, xxx+625 pp. | DOI | MR | Zbl

[2] A. A. Borovkov, Asimptoticheskii analiz sluchainykh bluzhdanii. Bystro ubyvayuschie raspredeleniya priraschenii, Fizmatlit, M., 2013, 447 pp. | Zbl

[3] A. A. Borovkov, A. A. Mogul'skii, “Integro-local and integral theorems for sums of random variables with semiexponential distributions”, Siberian Math. J., 47:6 (2006), 990–1026 | DOI | MR | Zbl

[4] A. V. Nagaev, “Cramer large deviations when the extreme conjugate distribution is heavy-tailed”, Theory Probab. Appl., 43:3 (1999), 405–421 | DOI | DOI | MR | Zbl

[5] L. V. Rozovskii, “Estimate from below for large-deviation probabilities of a sum of independent random variables with finite variances”, J. Math. Sci. (N. Y.), 109:6 (2002), 2192–2209 | DOI | MR | Zbl

[6] L. Saulis, V. A. Statulevičius, Limit theorems for large deviations, Math. Appl. (Soviet Ser.), 73, Kluwer Acad. Publ., Dordrecht, 1991, viii+232 pp. | DOI | MR | MR | Zbl | Zbl

[7] S. G. Tkachuk, “Lokalnye predelnye teoremy, dopuskayuschie bolshie ukloneniya, v sluchae ustoichivykh predelnykh zakonov”, Izv. AN UzSSR. Ser. fiz.-matem. nauk, 17:2 (1973), 30–33 | MR | Zbl

[8] A. Ya. Khinchin, “Dve teoremy o stokhasticheskikh protsessakh s odnotipnymi prirascheniyami”, Matem. sb., 3(45):3 (1938), 577–584 | Zbl

[9] A. Araujo, E. Giné, The central limit theorem for real and Banach valued random variables, Wiley Ser. Probab. Math. Statist., John Wiley Sons, New York–Chichester–Brisbane, 1980, xiv+233 pp. | MR | Zbl

[10] R. A. Doney, “A large deviation local limit theorem”, Math. Proc. Cambridge Philos. Soc., 105:3 (1989), 575–577 | DOI | MR | Zbl

[11] N. H. Bingham, C. M. Goldie, J. L. Teugels, Regular variation, Encyclopedia Math. Appl., 27, Cambridge Univ. Press, Cambridge, 1987, xx+491 pp. | DOI | MR | Zbl

[12] A. Gut, Stopped random walks. Limit theorems and applications, Springer Ser. Oper. Res. Financ. Eng., 2nd ed., Springer, New York, 2009, xiv+263 pp. | DOI | MR | Zbl

[13] J. Steinebach, “Invariance principles for renewal processes when only moments of low order exist”, J. Multivariate Anal., 26:2 (1988), 166–183 | DOI | MR | Zbl