Publications (55)
A note on the Sun distribution
Thomas Simon
We investigate the analytical properties of the Sun random variable, which arises from the domain of attraction of certain storage models involving a maximum and a sum. In the…
Fonctions de Mittag-Leffler et processus de Lévy stables sans saut négatif
Thomas Simon
It is noticed that a certain transform of the Mittag-Leffler function Ea is completely monotone for a in [1,2]. Using the explicit expressions of its Bernstein density, an identity…
On cumulative Tsallis entropies
Guillaume Dulac, Thomas Simon
We investigate the cumulative Tsallis entropy, an information measure recently introduced as a cumulative version of the classical Tsallis differential entropy, which is itself a g…
Total positivity of a Cauchy kernel
Thomas Simon
We study the total positivity of the kernel $1/(x^2 + 2 \cos(Ï\a)xy +y^2).$ The case of infinite order is characterized by an application of Schoenberg's theorem. We then give nec…
On the absolute continuity of multidimensional Ornstein-Uhlenbeck processes
Thomas Simon
Let be a -dimensional Ornstein-Uhlenbeck process, solution of the S.D.E. $$\d X_t = AX_t \d t + \d B_t$$ where is a real matrix and a Lévy process witho…
Total positivity in stable semigroups
Thomas Simon
We characterize the total positivity in space-time of real strictly stable semigroups. In the positive case, this solves a problem which had been raised by Karlin. In the drifted C…