Related papers: Results for convergence rates associated with rene…

We discuss some applications of the Mittag-Leffler function and related probability distributions in the theory of renewal processes and continuous time random walks. In particular we show the asymptotic (long time) equivalence of a generic…

We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.

Convergence results for averages of independent replications of counting processes are established in a $p$-variation setting and under certain assumptions. Such convergence results can be combined with functional differentiability results…

For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach…

We consider a renewal-like recursion and prove that the solution is polynomially decaying asymptotically under suitable conditions. We prove similar results for the corresponding integral equation. In both cases coefficients and functions…

It is shown, that the exponential decrease of the energy spectra of the fragments with growing its energy, which does not depend from the fragment type, targets, projectiles and projectile energies, and which sometimes accompanied slight…

I show that whenever a system undergoes a reproducible macroscopic process the mutual distinguishability of macrostates, as measured by their relative entropy, diminishes. This extends the second law which regards only ordinary entropies,…

In this paper, we consider time-inhomogeneous branching processes and time-inhomogeneous birth-and-death processes, in which the offspring distribution and birth and death rates (respectively) vary in time. A classical result of branching…

We consider the contact process with dormancy, where wake-up times follow a renewal process. Without infection between dormant individuals, we show that the process under certain conditions grows at most logarithmically. On the other hand,…

In this paper we prove a sharp quantitative version of the Kendall's Theorem. The Kendal Theorem states that under some mild conditions imposed on a probability distribution on positive integers (i.e. probabilistic sequence) one can prove…

We present and establish large deviations principles for general multivariate renewal-reward processes associated with a classical discrete-time renewal process. A renewal-reward process describes a cumulative reward over time, supposing…

In this paper we consider the rate of convergence of solutions of a scalar ordinary differential equation which is a perturbed version of an autonomous equation with a globally stable equilibrium. Under weak assumptions on the nonlinear…

There exist important stochastic physical processes involving infinite mean waiting times. The mean divergence has dramatic consequences on the process dynamics. Fractal time random walks, a diffusion process, and subrecoil laser cooling, a…

In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…

We study the situations when the solution to a weighted stochastic recursion has a power law tail. To this end, we develop two complementary approaches, the first one extends Goldie's (1991) implicit renewal theorem to cover recursions on…

Many dynamical phenomena display a cyclic behavior, in the sense that time can be partitioned into units within which distributional aspects of a process are homogeneous. In this paper, we introduce a class of models - called conjugate…

We consider the linear growth-fragmentation equation arising in the modelling of cell division or polymerisation processes. For constant coefficients, we prove that the dynamics converges to the steady state with an exponential rate. The…

The role of geometrically infinitely divisible laws in renewal equations and superposition of renewal processes are explored here. Some examples are also discussed.

In this article we study a diophantine property of probability measures on R. We will always assume that the considered measures have an exponential moment and a drift. We link this property to the points in C close to the imaginary axis…

We consider renewal-type processes whose positive inter-renewal times may be dependent, non-identically distributed, and may have mixed distributions. We introduce a generalised intensity measure extending the classical hazard-rate…