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@article{THSP_2008_14_4_a6,
author = {Nadiia Zinchenko and Andrii Andrusiv},
title = {Risk process with stochastic premiums},
journal = {Teori\^a slu\v{c}ajnyh processov},
pages = {189--208},
publisher = {mathdoc},
volume = {14},
number = {4},
year = {2008},
language = {en},
url = {http://geodesic.mathdoc.fr/item/THSP_2008_14_4_a6/}
}
Nadiia Zinchenko; Andrii Andrusiv. Risk process with stochastic premiums. Teoriâ slučajnyh processov, Tome 14 (2008) no. 4, pp. 189-208. http://geodesic.mathdoc.fr/item/THSP_2008_14_4_a6/
[1] Alex, M., Steinebach, J., “Invariance principles for renewal processes and some applications”, Teor. Imovirnost. ta Matem. Statyst, 50 (1994), 22–54 | MR | Zbl
[2] Andrusiv, A.,Zinchenko N., “Estimates for ruin probabilities and invariance principle for Cramér-Lundberg model with stochastic premiums”, Prykladna Statist., Actuarna ta Financ. Matematyka, 2 (2004), 5–17
[3] Berkes, I, Dehling, H., Dobrovski, D., Philipp, W., “A strong approximation theorem for sums of random vectors in domain of attraction to a stable law”, Acta Math. Hung., 48:1-2 (1986), 161–172 | DOI | MR | Zbl
[4] Berkes, I., Dehling, H., “Almost sure and weak invariance principle for random variables attracted by a stable law”, Probab. Theory and Related Fields, 38:3 (1989), 331–353 | DOI | MR
[5] Billingsley, P., Convergence of Probability Measures, J.Wiley, New York, 1968 | MR | Zbl
[6] Boykov A. V., “Cramér-Lundberg model with stochastic premiums”, Teor. Veroyatnost. i Primenen., 47 (2002), 549–553 | DOI | MR
[7] Csörgő, M., Révész, P., Strong Approximation in Probability and Statistics, Acad. Press., New York, 1981 | MR
[8] Csörgő, M., Horváth, L., Weighted Approximation in Probability and Statistics, J.Wiley, New York, 1993 | MR
[9] El-Nouty, C., “On increments of fractional Brownian motion”, Statist. Probab. Letters, 41 (1999), 169–178 | DOI | MR | Zbl
[10] Embrechts, P., Klüppelberg, C., Mikosch, T., Modelling Extremal Events, Springer-Verlag, Berlin, 1997 | MR | Zbl
[11] Erdös, P., Rényi, A., “On a new law of large numbers”, J.Analyse Math., 23 (1970), 103–111 | DOI | MR | Zbl
[12] Frolov, A., “On one-side strong laws for large increments of sums”, Statis. Probab. Letters, 37 (1998), 155–165 | DOI | MR | Zbl
[13] Frolov, A., “On an asymptotic behavior of increments of the sums of independent random variables”, Dokl. Rus.Acad.Nauk, 372 (2000), 596–599 (Rus.) | MR | Zbl
[14] Gantert, N., “Functional Erdös-Rényi laws for semiexponential random variables”, Ann. Probab., 26 (1998), 1356–1369 | DOI | MR | Zbl
[15] Furrer, H., “Risk processes pertubed by $\alpha$-stable Lévy motion”, Scand. Actuarial. J., 1998, no. 1, 59–74 | DOI | MR | Zbl
[16] Furrur, H., Michna, Z., Weron, A., “Stable Lévy motion approximation in col lective risk theory”, Insurance Math. Econ., 20 (1997), 97–114 | DOI | MR
[17] Springer-Verlag, Berlin, 1975 | MR | Zbl
[18] Gilina L. C., “Estimation of ruin probability for some insurance model”, Prykladna Statist., Actuarna ta Financ.Matematyka, 1 (2000), 67–73
[19] Grandell J., Aspects of Risk Theory, Springer, Berlin, 1991 | MR | Zbl
[20] Gusak D. V., Limit problems for processes with independent increments in risk theoty, IM, Kyiv, 2007 | MR
[21] Gut, A., Stopped Random Walks, Springer, Berlin, 1988 | MR | Zbl
[22] Iglehart, D. L., “Diffusion approximation in collective risk theory”, J. Appl. Probab., 6, 285–292 | DOI | MR | Zbl
[23] Korolev, V., Bening, V., Shorgin, S., Mathematical Foundations of Risk Theory, Fizmatlit, Moscow, 2007 (Rus.)
[24] Lanzinger, H., Stadmüller, U., “Maxima of increments of partial sums for certain subexponential distributions”, Stoch.Proc.Appl., 86 (2000), 323–343 | DOI | MR
[25] Lin, Z. Y., Lu, C. R., Strong Limit Theorems, Kluwer Science Press, Hong Kong, 1992 | MR | Zbl
[26] Theory Probab. Math. Statist., 53 (1995) | MR | MR | Zbl
[27] Silvestrov, D., Limit Theorems for Randomly Stopped Stochastic Processes, Springer-Verlag, London, 2004 | MR | Zbl
[28] Skorokhod, A. V., Studies in the Theory of Random Processes, Kiev Univ., 1961 | MR | Zbl
[29] Strassen, V., “Almost sure behavior for sums of independent r.v. and martingales”, Pros. 5th Berkeley Symp.2, 1967, 315–343 | MR | Zbl
[30] Whitt, W., Stochastic-Processes Limits: An Introduction to Stochastic Process Limits and Their Application to Queues, Springer-Verlag, New York, 2002 | MR
[31] Theory Probab. Appl., 30 (1985) | MR
[32] Theory Probab. Appl., 32 (1987) | MR
[33] Theory Probab. Math. Statist., 58 (1998) | MR | Zbl | Zbl
[34] Theory Probab. Math. Statist., 63 (2001) | Zbl
[35] Zinchenko, N., “The strong invariance principle for renewal and randomly stopped processes”, Theory of Stoch.Processes, 13(29):4 (2007), 233–245 | MR
[36] Zinchenko, N., Safonova M., “Erdös-Rény type law for random sums with applications to claim amount process”, Journal of Numerical and Appl. Mathematics, 1(69) (2008), 246–264 | Zbl