Related papers: New Classes of Infinitely Divisible Distributions …
The Stieltjes classes play a significant role in the moment problem since they permit to expose an infinite family of probability distributions all having equal moments of all orders. Given a moment-indeterminate distribution, it may not be…
We study monotone and convex stochastic orders for processes with independent increments. Our contributions are twofold: First, we relate stochastic orders of the Poisson component to orders of their (generalized) L\'evy measures. The…
In this study, we establish a significant connection between certain subclasses of complex order univalent functions and the Mittag-Leffler-type Poisson distribution series. We provide criteria for these series to belong to the specific…
There is a growing interest in the so-called Bayesian Predictive Inference approach, which allows to perform Bayesian inference without specifying the likelihood and prior of the model, or the need of any MCMC. Instead, only a sequence of…
We analyze the Levy processes produced by means of two interconnected classes of non stable, infinitely divisible distribution: the Variance Gamma and the Student laws. While the Variance Gamma family is closed under convolution, the…
We study a new class of so-called quasi-infinitely divisible laws, which is a wide natural extension of the well known class of infinitely divisible laws through the L\'evy--Khinchine type representations. We are interested in criteria of…
The infinite (in both directions) sequence of the distributions $\mu^{(k)}$ of the stochastic integrals $\int_0^{\infty-}c^{-N_{t-}^{(k)}} dL_t^{(k)}$ for integers $k$ is investigated. Here $c>1$ and $(N_t^{(k)},L_t^{(k)})$, $t\geq0$, is a…
Discrete multiplicative turbulent cascades are described using a formalism involving infinitely divisible random measures. This permits to consider the continuous limit of a cascade developed on a continuum of scales, and to provide the…
A probability distribution is n-divisible if its nth convolution root exists. While modeling the dependence structure between several (re)insurance losses by an additive risk factor model, the infinite divisibility, that is the…
We show the equivalence of three properties for an infinitely divisible distribution: the subexponentiality of the density, the subexponentiality of the density of its L\'evy measure and the tail equivalence between the density and its…
We state some inequalities for m-divisible and infinite divisible characteristic functions. Basing on them we propose a statistical test for a distribution to be infinitely divisible. Keywords: infinite divisible distributions; statistical…
Continuing the study reported in Satheesh (2001),(math.PR/0304499 dated 01 May 2003) and Satheesh (2002)(math.PR/0305030 dated 02May 2003), here we study generalizations of infinitely divisible (ID) and max-infinitely divisible (MID) laws.…
We consider a class of probability measures $\mu_{s,r}^{\alpha}$ which have explicit Cauchy-Stieltjes transforms. This class includes a symmetric beta distribution, a free Poisson law and some beta distributions as special cases. Also, we…
We generalize the work of Roquette and Zassenhaus on the invariant part of the class groups to the relative class groups. Thereby, we can show some statistical results as follows. For abelian extensions over a fixed number field K, we show…
In this article, we analyze three classes of time-reversal of a Markov process with Gaussian noise on a manifold. We first unveil a commutativity constraint for the most general of these time-reversals to be well defined. Then we give a…
We give a extensive account of a recent new way of applying the Dirichlet form theory to random Poisson measures. The main application is to obtain existence of density for thelaws of random functionals of L\'evy processes or solutions of…
Discrete diffusion models have gained increasing attention for their ability to model complex distributions with tractable sampling and inference. However, the error analysis for discrete diffusion models remains less well-understood. In…
In 1964 R.Gangolli published a L\'{e}vy-Khintchine type formula which characterised $K$ bi-invariant infinitely divisible probability measures on a symmetric space $G/K$. His main tool was Harish-Chandra's spherical functions which he used…
In this paper, we introduce a new technique to study the distribution in residue classes of sets of integers with digit and sum-of-digits restrictions. From our main theorem, we derive a necessary and sufficient condition for integers with…
Random integral mappings $I^{h,r}_{(a,b]}$ give isomorphisms between the sub-semigroups of the classical $(ID, \ast)$ and the free-infinite divisible $(ID,\boxplus)$ probability measures. This allows us to introduce new examples of such…