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1
Content available remote A family of generalized gamma convoluted variables
Roynette R., Vallois P., Yor M.
Probability and Mathematical Statistics
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2009
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Vol. 29, Fasc. 2
181--204
EN
This paper consists of three parts: in the first part, we describe a family of generalized gamma convoluted (abbreviated as GGC) variables. In the second part, we use this description to prove that several r.v.’s, related to the length of excursions away from 0 for a recurrent linear diffusion on R+, are GGC. Finally, in the third part, we apply our results to the case of Bessel processes with dimension d = 2(1 − α), where 0 < d < 2 or 0 < α< 1.
2
Content available remote On the remarkable distributions of maxima of some fragments of the standard reflecting random walk and Brownian motion
Fujita T., Yor M.
Probability and Mathematical Statistics
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2007
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Vol. 27, Fasc. 1
89--104
EN
In this paper, we consider some distributions of maxima of excursions and related variables for standard random walk and Brownian motion. We discuss the infinite divisibility properties of these distributions and calculate their Lévy measures. Lastly we discuss Chung's remark related with Riemann's zeta functional equation.
3
Content available remote A warning about an independence property related to random Brownian scaling
Fujita T., Yor M.
Probability and Mathematical Statistics
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2007
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Vol. 27, Fasc. 1
105--108
EN
In this note, which develops a part of our paper [2], we consider independence properties between Brownian motion, after Brownian scaling on a random interval (a, b), and the length (b—a) of the interval. We indicate three examples for which the Brownian scaled process is independent of the corresponding length. On the other hand, we discuss a case where this independence property does not hold and investigate further results for that example.
4
Content available remote On a particular class of self-decomposable random variables : the durations of Bessel excursions straddling independent exponential times
Bertoin J., Fujita T., Roynette B., Yor M.
Probability and Mathematical Statistics
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2006
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Vol. 26, Fasc. 2
315--366
EN
The distributional properties of the duration of a recurrent Bessel process straddling an independent exponential time are studied in detail. Although our study may be considered as a particular case of Winkel’s in [25], the infinite divisibility structure of these Bessel durations is particularly rich and we develop algebraic properties for a family of random variables arising from the Lévy measures of these durations.
5
Content available remote Selfdecomposable laws associated with hyperbolic functions
Jurek Z. J., Yor M.
Probability and Mathematical Statistics
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2004
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Vol. 24, Fasc. 1
181--190
EN
It is shown that the hyperbolic functions can be associated with self-decomposable distributions (in short: SD probability distributions or Lévy class L of probability laws). Consequently, they admit associated background driving Lévy processes Y (BDLP’s Y). We interpret the distributions of Y (1) via Bessel squared processes, Bessel bridges and local times.
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