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A note on extremes of compound Poisson processes

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Języki publikacji
EN
Abstrakty
EN
We investigate the conditions on a compound Poisson process X(t) 0≤t≤1, under which the right tail of sup0≤t≤1 X(t) is equivalent to the tail of X(1). New examples for which this relation does not hold are given.
Słowa kluczowe
Rocznik
Strony
309--320
Opis fizyczny
Bibliogr. 10 poz.
Twórcy
autor
  • Departments of Mathematics and of Computer Science, Ben-Gurion University of the Negev Beer-Sheva, 84105, Israel
autor
  • Departments of Mathematics, Ben-Gurion University of the Negev Beer-Sheva, 84105, Israel
autor
  • Departments of Mathematics, Ben-Gurion University of the Negev Beer-Sheva, 84105, Israel
Bibliografia
  • [1] J. M. P. Albin, Extremes of totally skewed stable motion, Statist. Probab. Lett. 16 (1993), pp. 219-224.
  • [2] J. M. P. Albin and M. Sunden, On the asymptotic behaviour of Lévy processes. Part I: Subexponential and exponential processes, Stochastic Process. Appl. 119 (2009), pp. 281-304.
  • [3] S. Berman, The supremum of a process with stationary independent symmetric increments, Stochastic Process. Appl. 23 (1986), pp. 281-290.
  • [4] M. Braverman, Suprema of compound Poisson processes with light tails, Stochastic Process. Appl. 90 (2000), pp. 145-156.
  • [5] M. Braverman and G. Samorodnitsky, Functionals of infinitely divisible stochastic processes with exponential tails, Stochastic Process. Appl. 56 (1995), pp. 207-231.
  • [6] P. Embrechts and C. M. Goldie, On closure and factorization properties of subexponential and related distributions, J. Aust. Math. Soc. Ser. A 29 (1980), pp. 243-256.
  • [7] I. Gikhman and A. Skorohod, Introduction to the Theory of Stochastic Processes, Dover, Mineola, NY, 1996.
  • [8] M. B. Marcus, »-radical Processes and Random Fourier Series, Mem. Amer. Math. Soc. 368, Amer. Math. Soc., Providence, RI, 1987.
  • [9] J. Rosiński and G. Samorodnitsky, Distributions of subadditive functionals of sample paths of infinitely divisible processes, Ann. Probab. 21 (1993), pp. 996-1014.
  • [10] E. Willekens, On the supremum of an infinitely divisible process, Stochastic Process. Appl. 26 (1987), pp. 173-175.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-bc4eb498-62a5-4ea7-b012-a3431659deaf
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