papers

Publications (55)

math.PR2023

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…

math.PR2009

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…

math.ST2023

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…

math.CA2013

Total positivity of a Cauchy kernel

Thomas Simon

We study the total positivity of the kernel $1/(x^2 + 2 \cos(π\a)xy +y^2).$ The case of infinite order is characterized by an application of Schoenberg's theorem. We then give nec…

math.PR2009

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…

math.CA2014

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…