메뉴 건너뛰기




Volumn 14, Issue 2, 2004, Pages 820-844

On overload in a storage model, with a self-similar and infinitely divisible input

Author keywords

Heavy tails; Infinitely divisible process; L vy process; Self similar process; Stable process; Stationary increment process; Storage process; Subexponential distribution

Indexed keywords


EID: 8544267250     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/105051604000000125     Document Type: Article
Times cited : (14)

References (23)
  • 1
    • 0032389950 scopus 로고    scopus 로고
    • Extremal theory for self-similar processes
    • ALBIN, J. M. P. (1998). Extremal theory for self-similar processes. Ann. Probab. 26 743-793.
    • (1998) Ann. Probab. , vol.26 , pp. 743-793
    • Albin, J.M.P.1
  • 2
    • 0033070982 scopus 로고    scopus 로고
    • Extremes of totally skewed α-stable processes
    • ALBIN, J. M. P. (1999). Extremes of totally skewed α-stable processes. Stochastic Process. Appl. 79 185-212.
    • (1999) Stochastic Process. Appl. , vol.79 , pp. 185-212
    • Albin, J.M.P.1
  • 3
    • 0000808359 scopus 로고
    • Variants on the law of the iterated logarithm
    • BINGHAM, N. H. (1986). Variants on the law of the iterated logarithm. Bull. London Math. Soc. 18 433-467.
    • (1986) Bull. London Math. Soc. , vol.18 , pp. 433-467
    • Bingham, N.H.1
  • 8
    • 0033210499 scopus 로고    scopus 로고
    • Extremes of a certain class of Gaussian processes
    • HÜSLER, J. and PITERBARG, V. (1999). Extremes of a certain class of Gaussian processes. Stochastic Process. Appl. 83 257-271.
    • (1999) Stochastic Process. Appl. , vol.83 , pp. 257-271
    • Hüsler, J.1    Piterbarg, V.2
  • 9
    • 4243993421 scopus 로고
    • Self-similar stable processes with stationary increments
    • (S. Cambanis, G. Samorodnitsky and M. S. Taqqu, eds.). Birkhäuser, Boston
    • KÔNO, N. and MAEJIMA, M. (1991). Self-similar stable processes with stationary increments. In Stable Processes and Related Topics (S. Cambanis, G. Samorodnitsky and M. S. Taqqu, eds.). Birkhäuser, Boston.
    • (1991) Stable Processes and Related Topics
    • Kôno, N.1    Maejima, M.2
  • 10
    • 84968515060 scopus 로고
    • Semi-stable stochastic processes
    • LAAMPERTI, J. W. (1962). Semi-stable stochastic processes. Trans. Amer. Math. Soc. 104 62-78.
    • (1962) Trans. Amer. Math. Soc. , vol.104 , pp. 62-78
    • Laamperti, J.W.1
  • 11
    • 0003033947 scopus 로고
    • Infinitely divisible processes
    • MARUYAMA, G. (1970). Infinitely divisible processes. Theory Probab. Appl. 15 1-22.
    • (1970) Theory Probab. Appl. , vol.15 , pp. 1-22
    • Maruyama, G.1
  • 12
    • 21344482808 scopus 로고
    • A storage model with self-similar input
    • NORROS, I. (1994). A storage model with self-similar input. Queuing Systems 16 387-396.
    • (1994) Queuing Systems , vol.16 , pp. 387-396
    • Norros, I.1
  • 13
    • 0036022582 scopus 로고    scopus 로고
    • Decomposition of self-similar stable mixing moving averages
    • PIPIRAS, V. and TAQQU, M. S. (2002a). Decomposition of self-similar stable mixing moving averages. Probab. Theory Related Fields 123 412-452.
    • (2002) Probab. Theory Related Fields , vol.123 , pp. 412-452
    • Pipiras, V.1    Taqqu, M.S.2
  • 14
    • 0036018204 scopus 로고    scopus 로고
    • The structure of self-similar stable mixing moving averages
    • PIPIRAS, V. and TAQQU, M. S. (2002b). The structure of self-similar stable mixing moving averages. Ann. Probab. 30 898-932.
    • (2002) Ann. Probab. , vol.30 , pp. 898-932
    • Pipiras, V.1    Taqqu, M.S.2
  • 15
    • 8544278050 scopus 로고    scopus 로고
    • Large deviations of a storage process with fractional Brownian motion as input
    • PITERBARG, V. I. (2001). Large deviations of a storage process with fractional Brownian motion as input. Extremes 4 147-164.
    • (2001) Extremes , vol.4 , pp. 147-164
    • Piterbarg, V.I.1
  • 16
    • 0001294305 scopus 로고
    • Spectral representations of infinite divisible processes
    • RAJPUT, B. S. and ROSINSKI, J. (1989). Spectral representations of infinite divisible processes. Probab. Theory Related Fields 82 451-487.
    • (1989) Probab. Theory Related Fields , vol.82 , pp. 451-487
    • Rajput, B.S.1    Rosinski, J.2
  • 17
    • 0000945009 scopus 로고
    • Distributions of subadditive functionals of sample paths of infinitely divisible processes
    • ROSIŃSKI, J. and SAMORODNITSKY, G. (1993). Distributions of subadditive functionals of sample paths of infinitely divisible processes. Ann. Probab. 21 996-1014.
    • (1993) Ann. Probab. , vol.21 , pp. 996-1014
    • Rosiński, J.1    Samorodnitsky, G.2
  • 18
  • 19
    • 0001375407 scopus 로고
    • (1/α)-self-similar processes with stationary increments
    • SAMORODNITSKY, G. and TAQQU, M. S. (1990). (1/α)-self-similar processes with stationary increments. J. Multivariate Anal. 35 308-313.
    • (1990) J. Multivariate Anal. , vol.35 , pp. 308-313
    • Samorodnitsky, G.1    Taqqu, M.S.2
  • 23
    • 0039999914 scopus 로고
    • Small tails for the supremum of a Gaussian process
    • TALAGRAND, M. (1988). Small tails for the supremum of a Gaussian process. Ann. Inst. H. Poincaré Sect. B 24 307-315.
    • (1988) Ann. Inst. H. Poincaré Sect. B , vol.24 , pp. 307-315
    • Talagrand, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.