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2 results

On moments and tail behaviors of storage processes
Part of
Arturo Kohatsu-Higa, Makoto Yamazato
Journal:

Journal of Applied Probability / Volume 40 / Issue 4 / September 2003

Published online by Cambridge University Press:

14 July 2016, pp. 1069-1086

Print publication:

September 2003
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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.

An asymptotic expansion for the expectation of an age-dependent branching process with a submultiplicative estimate of the remainder
Part of
- Markov processes
- Special processes
M. S. Sgibnev
Journal:

Journal of Applied Probability / Volume 38 / Issue 3 / September 2001

Published online by Cambridge University Press:

14 July 2016, pp. 807-814

Print publication:

September 2001
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An asymptotic expansion for the expected number, μ(t), of particles of an age-dependent branching process is obtained with a general submultiplicative estimate for the remainder term. The influence of the roots of the characteristic equation on the asymptotic behaviour of μ(t) is taken into account.

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2 results

On moments and tail behaviors of storage processes

An asymptotic expansion for the expectation of an age-dependent branching process with a submultiplicative estimate of the remainder