Geodesic
Integro-local limit theorems for compound renewal processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 2, pp. 217-240 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain integro-local theorems (analogues of Stone's theorem) for compound renewal processes when at least one of the following two conditions is met: (a) the components of the jumps in the process are independent or are linearly dependent, or (b) the jumps have finite moments of an order higher than 2. In case (b) we obtain an upper bound for the remainder term.
Keywords: compound renewal process, integro-local theorem, analogues of Stone's theorem. 
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A. A. Borovkov. Integro-local limit theorems for compound renewal processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 2, pp. 217-240. http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a0/

[1] D. R. Koks, V. L. Smit, Teoriya vosstanovleniya, Sovetskoe radio, M., 1967, 299 pp. ; D. R. Cox, Renewal theory, Methuen Co. Ltd., London; John Wiley Sons, Inc., New York, 1962, ix+142 с. ; W. L. Smith, “Renewal theory and its ramifications”, J. Roy. Statist. Soc. Ser. B, 20:2 (1958), 243–302 | MR | Zbl | MR | Zbl | MR | Zbl

[2] S. Asmussen, H. Albrecher, Ruin probabilities, Adv. Ser. Stat. Sci. Appl. Probab., 14, 2nd ed., World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2010, xviii+602 pp. | DOI | MR | Zbl

[3] A. A. Borovkov, Probability theory, Universitext, Springer, London, 2013, xxviii+733 pp. | DOI | MR | Zbl

[4] F. J. Anscombe, “Large-sample theory of sequential estimation”, Proc. Cambridge Philos. Soc., 48:4 (1952), 600–607 | DOI | MR | Zbl

[5] A. A. Borovkov, “Integral theorems for the first passage time of an arbitrary boundary by a compound renewal process”, Siberian Math. J., 56:5 (2015), 765–782 | DOI | DOI | MR | Zbl

[6] 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

[7] A. A. Borovkov, “Obobschenie i utochnenie integro-lokalnoi teoremy Stouna dlya summ sluchainykh vektorov”, Teoriya veroyatn. i ee primen., 61:4 (2016), 659–685 | DOI