In this work we analyze a class of diminishing 2 × 2 Pólya-Eggenberger urn models with ball replacement matrix M given by M = ` −a 0 c −d´, a, d ∈ N and c ∈ N0. We obtain limit laws for this class of 2 × 2 urns by giving estimates for the moments of the considered random variables. As a special instance we obtain limit laws for the pills problem, proposed by Knuth and McCarthy, which correspond...

Local limit theorems are derived for the number of occupied urns in general finite and infinite urn models under the minimum condition that the variance tends to infinity. Our results represent an optimal improvement over previous ones for normal approximation.

In this paper, we introduce the application of rigorous analysis procedures to goal models in order to provide several benefits beyond the initial act of modelling. Such analysis can allow modellers to assess the satisfaction of goals, facilitate evaluation of high-level design alternatives, help analysts decide on the high-level requirements and design of the system, test the sanity of a model...

This paper shows how one can use the theory of hidden Markov models for portfolio optimization. We illustrate our method by a ball and urn experiment. An application to historical data is examined.

Adaptive randomly reinforced urn (ARRU) is a two-color urn model where the updating process is defined by a sequence of non-negative random vectors {(D1,n, D2,n);n ≥ 1} and randomly evolving thresholds which utilize accruing statistical information for the updates. Let m1 = E[D1,n] and m2 = E[D2,n]. In this paper we undertake a detailed study of the dynamics of the ARRU model. First, for the ca...

When attempting to draw a ball of a specified color either from an urn containing 50 red balls and 50 black balls or from an urn containing an unknown ratio of 100 red and black balls, a majority of decision makers prefer the known-risk urn, and this ambiguity aversion effect violates expected utility theory. In an experimental investigation of the effect of urn size on ambiguity aversion, 149 ...

The models surveyed include generalized Pólya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided of some proofs. Applications are discussed in statistics, biology, economics and a number of other areas. AMS 2000 subject classifications: Primary 60J20, 60G50; secondary 37A50.