Extremes of subexponential Lévy driven moving average processes

Stochastic Processes and their Applications

Volumn 116, Issue 7, 2006, Pages 1066-1087

  Fasen, Vicky ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Continuous time MA process; Extreme value theory; Gumbel distribution; L vy process; Marked point process; Ornstein Uhlenbeck process; Point process; Subexponential distribution; Tail behavior

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FINITE DIFFERENCE METHOD; FUNCTIONS; MATHEMATICAL MODELS; RANDOM PROCESSES;

CONTINUOUS-TIME MA PROCESS; EXTREME VALUE THEORY; GUMBEL DISTRIBUTION; LÉVY PROCESS; MARKED POINT PROCESS; ORNSTEIN-UHLENBECK PROCESS; POINT PROCESS; SUBEXPONENTIAL DISTRIBUTION; TAIL BEHAVIOR;

TIME VARYING SYSTEMS;

EID: 33744552061     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2006.01.001     Document Type: Article

References (24)

1. Applebaum D. Lévy Processes and Stochastic Calculus (2004), Cambridge University Press, Cambridge
2. Sato K. Lévy Processes and Infinitely Divisible Distributions (1999), Cambridge University Press, Cambridge
3. Brockwell P.J. Heavy-tailed and non-linear continuous-time ARMA models for financial time series. In: Chan W.S., Li W.K., and Tong H. (Eds). Statistics and Finance (2000), Imperial College Press, London
4. Gushchin A.A., and Küchler U. On stationary solutions of delay differential equations driven by a Lévy process. Stochastic Process. Appl. 88 2 (2000) 195-211
5. Embrechts P., Klüppelberg C., and Mikosch T. Modelling Extremal Events for Insurance and Finance (1997), Springer, Berlin
6. Rootzén H. Extremes of moving averages of stable processes. Ann. Probab. 6 5 (1978) 847-869
7. Fasen V. Extremes of regularly varying mixed moving average processes. Adv. in Appl. Probab. 37 (2005) 993-1014
8. E. Willekens, Hogere orde theorie voor subexponentiële verdelingen, Ph.D. Thesis, Katholieke Universiteit Leuven, 1986
9. Goldie C.M., and Klüppelberg C. Subexponential distributions. In: Adler R.J., and Feldman R.E. (Eds). A Practical Guide to Heavy Tails: Statistical Techniques and Applications (1998), Birkhäuser, Boston 435-459
10. Cline D.B.H. Convolution tails, product tails and domains of attraction. Probab. Theory Related Fields 72 (1986) 529-557
11. Cline D.B.H., and Samorodnitsky G. Subexponentiality of the product of independent random variables. Stochastic Process. Appl. 49 1 (1994) 75-98
12. Pakes A.G. Convolution equivalence and infinite divisibility. J. Appl. Probab. 41 2 (2004) 407-424
13. A. Baltrunas, D.J. Daley, C. Klüppelberg, Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times, Stochastic Process. Appl. 111 (2) 237-258
14. Davis R., and Resnick S. Extremes of moving averages of random variables from the domain of attraction of the double exponential distribution. Stochastic Process. Appl. 30 1 (1988) 41-68
15. Rootzén H. Extreme value theory for moving average processes. Ann. Probab. 14 2 (1986) 612-652
16. Rajput B.S., and Rosinski J. Spectral representations of infinitely divisible processes. Probab. Theory Related Fields 82 3 (1989) 453-487
17. V. Fasen, Extremes of Lévy driven MA processes with applications in finance, Ph.D. Thesis, Munich University of Technology, December, 2004
18. Resnick S.I. Extreme Values, Regular Variation, and Point Processes (1987), Springer, New York
19. Daley D.J., and Vere-Jones D. An Introduction to the Theory of Point Processes. Elementary Theory and Methods. 2nd edition Vol. I (2003), Springer, New York
20. Kallenberg O. Foundations of Modern Probability (1997), Springer, New York
21. Lebedev A.V. Extremes of subexponential shot noise. Math. Notes 71 2 (2000) 206-210
22. Hsing T., and Teugels J.L. Extremal properties of shot noise processes. Adv. in Appl. Probab. 21 (1989) 513-525
23. Goldie C.M., and Resnick S. Subexponential distribution tails and point processes. Commun. Statist.-Stochastic Models 4 2 (1988) 361-372
24. Braverman M., and Samorodnitsky G. Functionals of infinitely divisible stochastic processes with exponential tails. Stochastic Process. Appl. 56 2 (1995) 207-231