Related papers: Classes of infinitely divisible distributions on R…
We consider a new class $\boldsymbol{Q}$ of distribution functions $F$ that have the property of rational-infinite divisibility: there exist some infinitely divisible distribution functions $F_1$ and $F_2$ such that $F_1=F*F_2$. A…
In this article, we give some reviews concerning negative probabilities model and quasi-infinitely divisible at the beginning. We next extend Feller's characterization of discrete infinitely divisible distributions to signed discrete…
Inspired by R. Speicher's multidimensional free central limit theorem and semicircle families, we prove an infinite dimensional compound Poisson limit theorem in free probability, and define infinite dimensional compound free Poisson…
We develop two novel approaches for constructing skewed and bimodal flexible distributions that can effectively generalize classical symmetric distributions. We illustrate the application of introduced techniques by extending normal,…
We show that, under the long-tailedness of the densities of normalized L\'evy measures, the densities of infinitely divisible distributions on the half line are subexponential if and only if the densities of their normalized L\'evy measures…
We consider a new class $\boldsymbol{Q}$ of distribution functions $F$ that have the property of rational-infinite divisibility: there exist some infinitely divisible distribution functions $F_1$ and $F_2$ such that $F_1=F*F_2$. A…
This article deals with IDT processes, i.e. processes which are infinitely divisible with respect to time. Given an IDT process $(X_{t},\,t\geq0)$, there exists a unique (in law) L\'evy process $(L_{t}; t\geq0)$ which has the same…
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…
It is shown that the hyperbolic functions can be associated with selfdecomposable distributions (in short: SD probability distributions or L\'evy class L probability laws). Consequently, they admit associated background driving L\'evy…
A quasi-infinitely divisible distribution on $\mathbb{R}^d$ is a probability distribution $\mu$ on $\mathbb{R}^d$ whose characteristic function can be written as the quotient of the characteristic functions of two infinitely divisible…
Inspired by the notion of quasi-infinite divisibility (QID), we introduce and study the class of freely quasi-infinitely divisible (FQID) distributions on $\mathbb{R}$, i.e. distributions which admit the free L\'{e}vy-Khintchine-type…
In this note we discuss the nature of gaps in the support of a discretely infinitely divisible distribution from the angle of compound Poisson laws/processes. The discussion is extended to infinitely divisible distributions on the…
A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite…
Continuing the study reported in Satheesh (2001),(arXiv:math.PR/0304499 dated 01May2003) here we study certain aspects of randomization in infinitely divisible (ID) and max-infinitely divisible (MID) laws. They generalize ID and MID laws.…
We show that a conditional characteristic function of generalized L\'evy stochastic areas can be viewed as a product a selfdecomposable distribution (i.e., L\'evy class L distribution) and its background driving characteristic function.…
Consider a class of probability distributions which is dense in the space of all probability distributions on $\mathbb{R}^{d}$ with respect to weak convergence, for every $d\in\mathbb{N}$. Then, we construct various explicit classes of…
We prove that the classical normal distribution is infinitely divisible with respect to the free additive convolution. We study the Voiculescu transform first by giving a survey of its combinatorial implications and then analytically,…
We connect shift-invariant characteristic kernels to infinitely divisible distributions on $\mathbb{R}^{d}$. Characteristic kernels play an important role in machine learning applications with their kernel means to distinguish any two…
We establish a one-to-one correspondence between (i) exchangeable sequences of random variables whose finite-dimensional distributions are minimum (or maximum) infinitely divisible and (ii) non-negative, non-decreasing, infinitely divisible…
The role of geometrically infinitely divisible laws in renewal equations and superposition of renewal processes are explored here. Some examples are also discussed.