Geodesic
Unified limit theorems for increments of processes with independent increments
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 3, pp. 601-609 Cet article a éte moissonné depuis la source Math-Net.Ru

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A unified theory is constructed which describes the a.s. (almost surely) behavior of increments of stochastically continuous homogeneous processes with independent increments. This theory includes the strong law of large numbers, the Erdös–Rényi law, the Shepp law, the Csörgő–Révész law, and the law of the iterated logarithm. The range of applicability of the results is extended from several particular cases to the whole class of stochastically continuous homogeneous processes with independent increments.
Keywords: increments of processes with independent increments, Erdös–Rényi law, Shepp law, the law of large numbers, the law of the iterated logarithm. 
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A. N. Frolov. Unified limit theorems for increments of processes with independent increments. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 3, pp. 601-609. http://geodesic.mathdoc.fr/item/TVP_2004_49_3_a10/

[1] Shepp L. A., “A limit law concerning moving averages”, Ann. Math. Statist., 35 (1964), 424–428 | DOI | MR | Zbl

[2] Erdős P., Rényi A., “On a new law of large numbers”, J. Anal. Math., 23 (1970), 103–111 | DOI | MR | Zbl

[3] Csörgő S., “Erdős–Rényi laws”, Ann. Statist., 7:4 (1979), 772–787 | DOI | MR | Zbl

[4] Deheuvels P., Devroye L., “Limit laws of Erdős–Rényi–Shepp type”, Ann. Probab., 15:4 (1987), 1363–1386 | DOI | MR | Zbl

[5] Mason D. M., “An extended version of the Erdős–Rényi strong law of large numbers”, Ann. Probab., 17:1 (1989), 257–265 | DOI | MR | Zbl

[6] Csörgő M., Révész P., Strong Approximations in Probability and Statistics, Academic Press, New York, London, 1981, 284 pp. | MR | Zbl

[7] Frolov A. N., “On one-sided strong laws for large increments of sums”, Statist. Probab. Lett., 37:2 (1998), 155–165 | DOI | MR | Zbl

[8] Frolov A. N., “Ob asimptoticheskom povedenii priraschenii summ nezavisimykh sluchainykh velichin”, Dokl. RAN, 372:5 (2000), 596–599 | MR | Zbl

[9] Frolov A. N., “One-sided strong laws for increments of sums of i.i.d. random variables”, Studia Sci. Math. Hungar., 39:3–4 (2002), 333–359 | MR | Zbl

[10] Deheuvels P., Steinebach J., “Sharp rates for increments of renewal processes”, Ann. Probab., 17:2 (1989), 700–722 | DOI | MR | Zbl

[11] Steinebach J., “Strong laws for small increments of renewal processes”, Ann. Probab., 19:4 (1991), 1768–1776 | DOI | MR | Zbl

[12] Zinchenko N. M., “Asimptotika priraschenii ustoichivykh sluchainykh protsessov so skachkami odnogo znaka”, Teoriya veroyatn. i ee primen., 32:4 (1987), 793–796 | MR

[13] Borovkov A. A., Teoriya veroyatnostei, Nauka, M., 1986, 431 pp. | MR | Zbl

[14] Ibragimov I. A., Linnik Yu. V., Nezavisimye i statsionarno svyazannye velichiny, Nauka, M., 1965, 524 pp.

[15] Gikhman I. I., Skorokhod A. V., Teoriya sluchainykh protsessov, v. 2, Nauka, M., 1973, 640 pp. | MR

[16] Petrov V. V., Predelnye teoremy dlya summ nezavisimykh sluchainykh velichin, Nauka, M., 1987, 317 pp. | MR