Related papers: Fluctuations of balanced urns with infinitely many…

Our main result is to prove almost-sure convergence of a stochastic-approximation algorithm defined on the space of measures on a non-compact space. Our motivation is to apply this result to measure-valued P\'olya processes (MVPPs, also…

We consider a version of the classical P\'olya urn scheme which incorporates innovations. The space $S$ of colors is an arbitrary measurable set. After each sampling of a ball in the urn, one returns $C$ balls of the same color and…

A classical P\'olya urn scheme is a Markov process whose evolution is encoded by a replacement matrix $(R_{i,j})_{1\leq i,j\leq d}$. At every discrete time-step, we draw a ball uniformly at random, denote its colour $c$, and replace it in…

Measure-valued P\'olya urn sequences (MVPS) are a generalization of the observation processes generated by $k$-color P\'olya urn models, where the space of colors $\mathbb{X}$ is a complete separable metric space and the urn composition is…

We consider a model of N two-colors urns in which the reinforcement of each urn depends also on the content of all the other urns. This interaction is of mean-field type and it is tuned by a parameter $\alpha$ in [0,1]; in particular, for…

We consider the generalization of the P\'olya urn scheme with possibly infinite many colors as introduced in \cite{Th-Thesis, BaTH2014, BaTh2016, BaTh2017}. For countable many colors, we prove almost sure convergence of the urn…

A P\'olya urn process is a Markov chain that models the evolution of an urn containing some coloured balls, the set of possible colours being $\{1,\ldots,d\}$ for $d\in \mathbb{N}$. At each time step, a random ball is chosen uniformly in…

We consider the general version of P\'olya urns recently studied by Bandyopadhyay and Thacker (2016+) and Mailler and Marckert (2017), with the space of colours being any Borel space $S$ and the state of the urn being a finite measure on…

In this paper, we prove functional limit theorems for P\'olya urn processes whose number of draws and initial number of balls tend to infinity together. This is motivated by recent work of Borovkov [5], where they prove a functional limit…

P\'olya urns are urns where at each unit of time a ball is drawn and replaced with some other balls according to its colour. We introduce a more general model: the replacement rule depends on the colour of the drawn ball and the value of…

We define and prove limit results for a class of dominant P\'olya sequences, which are randomly reinforced urn processes with color-specific random weights and unbounded number of possible colors. Under fairly mild assumptions on the…

Motivated by mathematical tissue growth modelling, we consider the problem of approximating the dynamics of multicolor P\'olya urn processes that start with large numbers of balls of different colors and run for a long time. Using strong…

We study a P\'olya-type urn model defined as follows. Start at time 0 with a single ball of some colour. Then, at each time n>0, choose a ball from the urn uniformly at random. With probability 1/2<p<1, return the ball to the urn along with…

We give bounds for (central) moments for balanced P\'olya urns under very general conditions. In some cases, these bounds imply that moment convergence holds in earlier known results on asymptotic distribution. The results overlap with…

In this paper, we consider a new type of urn scheme, where the selection probabilities are proportional to a weight function, which is linear but decreasing in the proportion of existing colours. We refer to it as the \emph{negatively…

In this work we consider the \emph{infinite color urn model} associated with a bounded increment random walk on $\Zbold^d$. This model was first introduced by Bandyopadhyay and Thacker (2013). We prove that the rate of convergence of the…

It is known that in an irreducible small P\'olya urn process, the composition of the urn after suitable normalization converges in distribution to a normal distribution. We show that if the urn also is balanced, this normal convergence…

We introduce a modification of the generalized P\'olya urn model containing two urns and we study the number of balls $B_j(n)$ of a given color $j\in\{1,\ldots,J\}$, $J\in\mathbb{N}$ added to the urns after $n$ draws. We provide sufficient…

We consider triangular P\'olya urns and show under very weak conditions a general strong limit theorem of the form $X_{ni}/a_{ni}\to \mathcal{X}_i$ a.s., where $X_{ni}$ is the number of balls of colour $i$ after $n$ draws; the constants…

In a recent paper, the authors studied the distribution properties of a class of exchangeable processes, called measure-valued P\'{o}lya sequences (MVPS), which arise as the observation process in a generalized urn sampling scheme. Here we…