Related papers: The Dickman subordinator, renewal theorems, and di…
In this article densities (and their derivatives) of subordinators and inverse subordinators are considered. Under minor restrictions, generally milder than the existing in the literature, using a useful modification of the saddle point…
The one-dimensional Dickman distribution arises in various stochastic models across number theory, combinatorics, physics, and biology. Recently, a definition of the multidimensional Dickman distribution has appeared in the literature,…
A regenerative composition structure is a sequence of ordered partitions derived from the range of a subordinator by a natural sampling procedure. In this paper, we extend previous studies Barbour and Gnedin (2006), Gnedin, Iksanov and…
An interesting line of research is the investigation of the laws of random variables known as Dirichlet means. However, there is not much information on interrelationships between different Dirichlet means. Here, we introduce two…
For subordinators with positive drift we extend recent results on the structure of the potential measures and the renewal densities. Applying Fourier analysis a new representation of the potential densities is derived from which we deduce…
In this paper, we discuss estimates on transition densities for subordinators, which are global in time. We establish the sharp two-sided estimates on the transition densities for subordinators whose L\'evy measures are absolutely…
We prove existence and asymptotic behavior of the transition density for a large class of subordinators whose Laplace exponents satisfy lower scaling condition at infinity. Furthermore, we present lower and upper bounds for the density.…
We start by defining a subordinator by means of the lower-incomplete gamma function. It can be considered as an approximation of the stable subordinator, easier to be handled thank to its finite activity. A tempered version is also…
We study one-dimensional Levy processes with Levy-Khintchine exponent psi(xi^2), where psi is a complete Bernstein function. These processes are subordinate Brownian motions corresponding to subordinators, whose Levy measure has completely…
We consider a general model of a heterogeneous polymer chain fluctuating in the proximity of an interface between two selective solvents. The heterogeneous character of the model comes from the fact that the monomer units interact with the…
In this article, we introduce Mittag-Leffler L\'evy process and provide two alternative representations of this process. First, in terms of Laplace transform of the marginal densities and next as a subordinated stochastic process. Both…
Renewal theorems are developed for point processes with interarrival times $W_n=\xi(X_{n+1}X_n\cdots)$, where $(X_n)_{n\in\mathbb Z}$ is a stochastic process with finite state space $\Sigma$ and $\xi\colon\Sigma_A\to\mathbb R$ is a H\"older…
There exist only a few known examples of subordinators for which the transition probability density can be computed explicitly along side an expression for its L\'evy measure and Laplace exponent. Such examples are useful in several areas…
It is known that the exponential functional of a Poisson process admits a probability density function in the form of an infinite series. In this paper, we obtain an explicit expression for the density function of the exponential functional…
In this paper we establish local estimates for the first passage time of a subordinator under the assumption that it belongs to the Feller class, either at zero or infinity, having as a particular case the subordinators which are in the…
In this paper, we consider transient subordinate Brownian motion X in R^d, d \geq 1, where the Laplace exponent \phi of the corresponding subordinator satisfies some mild conditions. The scaleinvariant Harnack inequality is proved for X. We…
The purpose of this note is to prove the celebrated Discrete Renewal Theorem in a common special case. We use only very elementary methods from real analysis, rather than markov chain theory, complex analysis, or generating functions.…
We consider the first-hitting time of a tempered $\beta$-stable subordinator, also called inverse tempered stable (ITS) subordinator. The density function of the ITS subordinator is obtained, for the index of stability $\beta \in (0,1)$.…
The study of distributed order calculus usually concerns about fractional derivatives of the form $\int_0^1 \partial^\alpha u \, m(d\alpha)$ for some measure $m$, eventually a probability measure. In this paper an approach based on L\'evy…
We consider a class of tempered subordinators, namely a class of subordinators with one-dimensional marginal tempered distributions which belong to a family studied in [3]. The main contribution in this paper is a non-central moderate…