Lévy-type stochastic integrals with regularly varying tails

Stochastic Analysis and Applications

Volumn 23, Issue 3, 2005, Pages 595-611

  Applebaum, David ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

L vy measure; L vy type stochastic integral; Predictable mapping; Regular variation; Semimartingale

Indexed keywords

EID: 20444430516     PISSN: 07362994     EISSN: None     Source Type: Journal    
DOI: 10.1081/SAP-200056692     Document Type: Article

References (21)

1. Akgiray, V., and G. G. Booth. 1988. The stable-law model of stock returns, Journal of Business and Economic Statistics 6:51-57.
2. Applebaum, D. 2004. Lévy Processes and Stochastic Calculus. Cambridge, UK: Cambridge University Press.
3. Basrak, B., R. A. Davis, and T. Mikosch. 2002. Regular variation of GARCH processes. Stoch. Proc. App. 99:95-115.
4. Bingham, N. H., C. M. Goldie, and J. L. Teugels. 1987. Regular Variation. Cambridge, UK: Cambridge University Press.
5. Embrechts, P., C. M. Goldie, and N. Veraverbeke. Subexponentiality and infinite divisibility. Z Wahrscheinlichkeitstheorie verw. Gebiete 49:335-47.
6. Embrechts, P., and C. M. Goldie. 1980. On closure and factorization properties of subexponential and related distributions. J. Austral Math. Soc. (Series A) 29:243-56.
7. Embrechts, P., and C. M. Goldie. 1981. Comparing the tail of an infinitely divisible distribution with integrals of its Lévy measure. Ann. Prob. 9: 468-81.
8. Embrechts, P., C. Klüppelberg, and T. Mikosch. 1997. Modelling Extremal Events for Insurance and Finance. Berlin/Heidelberg: Springer-Verlag.
9. Feller, W. 1971. An Introduction to Probability Theory and Its Applications Volume 2 (second edition). New York, NY: John Wiley.
10. Ikeda, N., and S. Watanabe. 1989. Stochastic Differential Equations and Diffusion Processes (second edition). Amsterdam/New York: North Holland-Kodansha.
11. Kunita, H. 2004. Stochastic differential equations based on Lévy processes and stochastic flows of diffeomorphisms. To appear in Real and Stochastic Analysis, ed. M.M. Rao, Boston, Birkhouses.
12. Lindskog, F. 2004. Multivariate Extremes and Regular Variation for Stochastic Processes. Diss. ETH No. 15319.
13. Meerschaert, M. M., and H.-P. Scheffler. 2001. Limit Distributions for Sums of Independent Random Vectors. New York, NY: J. Wiley and Sons, Inc.
14. Meerschaert, M. M., and H.-P. Scheffler. 2003. Portfolio modelling with heavy tailed random vectors. In Handbook of Heavy Tailed Distributions in Finance, ed. S.T. Rachev, Elsevier, 595-640.
15. Resnick, S. 1986. Point processes, regular variation and weak convergence. Adv. Appl. Prob. 18:66-138.
16. Resnick, S. 1987. Extreme Values, Regular Variation and Point Processes. New York, NY: Springer-Verlag.
17. Resnick, S. 2004. On the foundations of multivariate heavy tail analysis. J. App. Prob. 41 A.
18. Rosiński, W. A. Woyczyński. 1986. On Itô stochastic integration with respect to p-stable motion: Inner clock, integrability of sample paths, double and multiple integrals. Ann. Prob. 14:271-86.
19. Samorodnitsky, G., and M. Grigoriu. 2003. Tails of solutions of stochastic differential equations driven by heavy tailed Lévy motions. Stoch. Proc. Applns 105:690-97.
20. Samorodnitsky, G. 2002. Long Range Dependence, Heavy Tails and Rare Events. Copenhagen Lecture Notes, MaPhySto; See http://www.maphysto. dk/cgi-bin/w3-msql/publications/genericpublication.html?publ=412.
21. Seneta, E. 1976. Regularly Varying Functions, Lecture Notes in Mathematics 508. Berlin/Heidelberg: Springer-Verlag.