Suprema and sojourn times of Lévy processes with exponential tails

Stochastic Processes and their Applications

Volumn 68, Issue 2, 1997, Pages 265-283

  Braverman, Michael ^a  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Exponential distributions; L vy process; Sojourn times

Indexed keywords

EID: 0031575039     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(97)00031-8     Document Type: Article

References (14)

1. Berman, S.M., 1986. The supremum of a process with stationary, independent and stationary increments. Stochatric Process Appl. 23, 281-290.
2. Berman, S.M., 1992. Sojourns and Extremes of Stochastic Processes. Wadsworth & Brooks, Belmont, CA.
3. Bertoin, J., Doney, R.A., 1993. Some asymptotic results for transient random walks, Tech. Rep. N0. 93/1, Statistical Laboratory, Department of Mathematics, University of Manchester.
4. Braverman, M., Samorodnitsky, G. 1995. Functionals of infinitely divisible stochastic processes with exponential tails. Stochastic Process Appl. 56, 207-231.
5. Chistyakov, V.P., 1964. A theorem on sums of independent random variables and its applictions to branching random processes. Theory Probab. Appl. 9, 640-648.
6. Chover, J., Ney, P., Wainger, S., 1973. Functions of probability measures. J. Anal. Math. 26, 255-302.
7. Cline, D.B.H., 1986. Convolution tails, product tails and domain of attraction. Probab. Theory Related Fields 72, 529-557.
8. Cline, D.H.B., 1987. Convolutions of distributions with exponential and subexponential tails. J. Austral. Math. Soc. Ser. 43, 347-365.
9. Embrechts, P., Goldie, C.M. 1982. On convolution tails. Stochastic Process. Appl. 13, 263-278.
10. Marcus, M.B., 1987. ξ-radial processes and random Fourier series. Mem. Amer. Math. Soc. 368.
11. Pollard, D., 1984. Convergence of Stochastic Processes. Springer, Berlin.
12. Rosiński, J., Samorodnitsky, G., 1993. Distribution of subadditive functionals of sample paths of infinitely divisible processes. Ann. Probab. 21, 996-1014.
13. Teugels, J.L., 1975. The class of subexponential distributions. Ann. Probab. 3, 1000-1011.
14. Willekens, E., 1987. On the supremum of an infinitely divisible process. Stochastic Process. Appl. 26, 173-175.