@article{TVP_2012_57_3_a6,
author = {K. A. Borovkov and G. Decrouez},
title = {Ornstein{\textendash}Uhlenbeck type processes with heavy distribution tails},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {533--559},
year = {2012},
volume = {57},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_2012_57_3_a6/}
}
K. A. Borovkov; G. Decrouez. Ornstein–Uhlenbeck type processes with heavy distribution tails. Teoriâ veroâtnostej i ee primeneniâ, Tome 57 (2012) no. 3, pp. 533-559. http://geodesic.mathdoc.fr/item/TVP_2012_57_3_a6/
[1] Adler R., Feldman R., Taqqu M. (eds.), A Practical Guide to Heavy Tails: Statistical Techniques and Applications, Birkhäuser, Boston, 1998, 533 pp. | MR
[2] Andersen T. G., Davis R. A., Kreiß J.-P., Mikosch T. (eds.), Handbook of Financial Time Series, Springer, Berlin, 2009, 1050 pp.
[3] Bibby B. M., Sorensen M., “A hyperbolic diffusion model for stock prices”, Finance Stoch., 1:1 (1996), 25–41 | DOI | MR
[4] Billingsley P., Probability and Measure, Wiley, New York, 1995, 593 pp. | MR | Zbl
[5] Borovkov A. A., Matematicheskaya statistika, Nauka, Novosibirsk, 1997, 771 pp. | MR
[6] Borovkov A. A., Borovkov K. A., Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions, Cambridge Univ. Press, Cambridge, 2008, 625 pp. | MR | Zbl
[7] Heyde C. C., Leonenko N. N., “Student processes”, Adv. in Appl. Probab., 37:2 (2005), 342–365 | DOI | MR | Zbl
[8] Hill B. M., “A simple general approach to inference about the tail of a distribution”, Ann. Statist., 3:5 (1975), 1163–1174 | DOI | MR | Zbl
[9] Jensen J. L., Pedersen J., “Ornstein–Uhlenbeck type processes with non-normal distribution”, J. Appl. Probab., 36:2 (1999), 389–402 | DOI | MR | Zbl
[10] Karlin S., Taylor H., A First Course in Stochastic Processes, Academic Press, New York, 1975, 557 pp. | MR | Zbl
[11] Kojadinovic I., Yan J., “A goodness-of-fit test for multivariate multiparameter copulas based on multiplier central limit theorems”, Statist. Comput., 21:1 (2010), 17–30 | DOI | MR
[12] Kojadinovic I., Yan J., “Modeling multivariate distributions with continuous margins using the copula R package”, J. Statist. Software, 34 (2010), 1–20
[13] McNeil A. J., Frey R., Embrechts P., Quantitative Risk Management: Concepts, Techniques and Tools, Princeton Univ. Press, Princeton, 2005 | MR | Zbl
[14] Maller R. A., Müller G., Szimayer A., “Ornstein–Uhlenbeck processes and extensions”, Handbook of Financial Time Series, eds. T. G. Andersen et al., Springer, New York, 2009, 421–438 | DOI
[15] Masuda H., “On multidimensional Ornstein–Uhlenbeck process driven by a general Lévy process”, Bernoulli, 10:1 (2004), 97–120 | DOI | MR | Zbl
[16] Protter P. E., Stochastic Integration and Differential Equations, Springer, Berlin, 2005, 419 pp. | MR
[17] Rachev S. T. (ed.), Handbook of Heavy Tailed Distributions in Finance, Elsevier, Amsterdam, 2003
[18] Ricciardi L. M., Sato S., “First-passage-time density and moments of the Ornstein–Uhlenbeck process”, J. Appl. Probab., 25 (1988), 43–57 | DOI | MR | Zbl
[19] Rootzen H., Leadbetter M., Haan L., Tail and quantile estimation for strongly mixing stationary sequences, Technical Report 292, Center for Stochastic Processes, Univ. of North Carolina, Chapel Hill, 1990
[20] Sato S., “Evaluation of the first-passage time probability to a square root boundary for the Wiener process”, J. Appl. Probab., 14 (1977), 850–856 | DOI | MR | Zbl