We study a new class of time inhomogeneous Pólya-type urn schemes and give optimal rates of convergence for the distribution of the properly scaled number of balls of a given color to nearly the full class of generalized gamma distributions with integer parameters, a class which includes the Rayleigh, half-normal and gamma distributions. Our main tool is Stein’s method combined with characteriz...

In this paper we obtain central limit theorems for generalized Pólya urn models with L ≥ 2 colors where one out ofK different replacements (actions) is applied randomly at each step. Each possible action constitutes a row of the replacement matrix, which can be nonsquare and random. The actions are chosen following a probability distribution given by an arbitrary function of the proportions of ...

In a one-parameter model for evolution of random trees, which also includes the Barabási–Albert random tree [1], almost sure behavior and the limiting distribution of the degree of a vertex in a fixed position are examined. A functional central limit theorem is also given. Results about Pólya urn models are applied in the proofs.

Bona [6] studied the distribution of ascents, plateaux and descents in the class of Stirling permutations, introduced by Gessel and Stanley [14]. Recently, Janson [18] showed the connection between Stirling permutations and plane recursive trees and proved a joint normal law for the parameters considered by Bona. Here we will consider generalized Stirling permutations extending the earlier resu...

We study several exactly solvable Pólya-Eggenberger urn models with a diminishing character, namely, balls of a specified color, say x are completely drawn after a finite number of draws. The main quantity of interest here is the number of balls left when balls of color x are completely removed. We consider several diminishing urns studied previously in the literature such as the pills problem,...

A multitype urn scheme with random replacements is considered. Each time a ball is picked, another ball is added, and its type is chosen according to the transition probabilities of a reducible Markov chain. The vector of frequencies is shown to converge almost surely to a random element of the set of stationary measures of the Markov chain. Its probability distribution is characterized as the ...

This paper describes examples of non-self averaging phenomena drawn from macroeconomic and physics fields. They are models of random clusters, such as Poisson-Dirichlet models, urn models, and models of random transport through disordered media. In particular, we discuss several three-parameter extension of the two parameter Poisson-Dirichlet model. These three parameter models inherit non-self...

User Requirements Notation (URN) is a modeling language with two complementary notations for capturing goals and non-functional requirements as well as low level processes and functional requirements. URN helps documenting the rationale behind the decisions, however, it lacks gathering the evidences for these rationales and documenting stakeholder discussions. In this paper, we propose a framew...

This article demonstrates how the User Requirements Notation (URN) can be used to model business processes. URN combines goals and scenarios in order to help capture and reason about user requirements prior to detailed design. In terms of application areas, this emerging standard targets reactive systems in general, with a particular focus on telecommunications systems and services. This articl...