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On moments and tail behaviors of storage processes

  • Arturo Kohatsu-Higa (a1) and Makoto Yamazato (a2)


We study the existence of moments and the tail behavior of the densities of storage processes. We give sufficient conditions for existence and nonexistence of moments using the integrability conditions of submultiplicative functions with respect to Lévy measures. We then study the asymptotical behavior of the tails of these processes using the concave or convex envelope of the release rate function.


Corresponding author

Postal address: Department of Economics, Universitat Pompeu Fabra, Ramón Trias Fargas, 25–27, 08005 Barcelona, Spain. Email address:
∗∗ Postal address: Department of Mathematics, Faculty of Science, University of the Ryukyus, Senbaru1, Nishihara-cho, Okinawa, Japan 903-0213.


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[1] Asmussen, S. (1998). Subexponential asymptotics for stochastic processes: extremal behaviour, stationary distributions and first passage probabilities. Ann. Appl. Prob. 8, 354374.
[2] Brockwell, P. J., Resnick, S. J., and Tweedie, R. L. (1982). Storage processes with general release rule and additive inputs. Adv. Appl. Prob. 14, 392433.
[3] Chistyakov, V. P. (1964). A theorem on sums of independent positive random variables and its applications to branching processes. Theory Prob. Appl. 9, 640648.
[4] Deshmukh, S. and Pliska, S. (1980). Optimal consumption and exploration of nonrenewable resources under uncertainty. Econometrica 48, 177200.
[5] Dharmadhicari, S., and Joag-dev, K. (1988). Unimodality, Convexity and Applications. Academic Press, San Diego, CA.
[6] Embrechts, P., Goldie, C. M., and Veraverbeke, N. (1979). Subexponentiality and infinite divisibility. Z. Wahrscheinlichkeitsth. 49, 335347.
[7] Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. 2, 2nd edn. John Wiley, New York.
[8] Grigoriu, M., and Samorodnitsky, G. (2002). Tails of solutions of certain nonlinear stochastic differential equations driven by heavy tailed Lévy motions. In Proc. 2nd MaPhySto Conf. Lévy Process. Theory Appl., MaPhySto, University of Aarhus, pp. 202205.
[9] Kendall, D. G. (1957). Some problems in the theory of dams. J. R. Statist. Soc. B 19, 207212.
[10] Rosinski, J. and Samorodnitsky, G. (1993). Distributions of subadditive functionals of sample paths of infinitely divisible processes. Ann. Prob. 21, 9961014.
[11] Sato, K. (1999). Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press.
[12] Sato, K., and Yamazato, M. (1984). Operator-self-decomposable distributions as limit distributions of processes of Ornstein—Uhlenbeck type. Stoch. Process. Appl. 17, 73100.
[13] Sigman, K., and Yao, D. (1994). Finite moments for inventory processes. Ann. Appl. Prob. 4, 765778.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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