Pólya urn schemes with infinitely many colors
A Bandyopadhyay, D Thacker - 2017 - projecteuclid.org
In this work, we introduce a class of balanced urn schemes with infinitely many colors
indexed by Z^d, where the replacement schemes are given by the transition matrices …
indexed by Z^d, where the replacement schemes are given by the transition matrices …
Almost sure and moment convergence for triangular P\'olya urns
S Janson - arXiv preprint arXiv:2402.01299, 2024 - arxiv.org
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 $ as, where $ X_ {ni} $ is the …
limit theorem of the form $ X_ {ni}/a_ {ni}\to\mathcal {X} _i $ as, where $ X_ {ni} $ is the …
Revisit of a Diaconis urn model
L Yang, J Hu, Z Bai - Stochastic Processes and their Applications, 2024 - Elsevier
Let G be a finite Abelian group of order d. We consider an urn in which, initially, there are
labeled balls that generate the group G. Choosing two balls from the urn with replacement …
labeled balls that generate the group G. Choosing two balls from the urn with replacement …
A New Approach to P\'olya Urn Schemes and Its Infinite Color Generalization
A Bandyopadhyay, D Thacker - arXiv preprint arXiv:1606.05317, 2016 - arxiv.org
In this work we generalize Polya urn schemes with possibly infinitely many colors and
extend the earlier models described in [4, 5, 7]. We provide a novel and unique approach of …
extend the earlier models described in [4, 5, 7]. We provide a novel and unique approach of …
Strong convergence of infinite color balanced urns under uniform ergodicity
A Bandyopadhyay, S Janson… - Journal of Applied …, 2020 - cambridge.org
We consider the generalization of the Pólya urn scheme with possibly infinitely many colors,
as introduced in [37],[4],[5], and [6]. For countably many colors, we prove almost sure …
as introduced in [37],[4],[5], and [6]. For countably many colors, we prove almost sure …
Investigating Multicolor Affine Urn Models with Multiple Drawings
JH Sparks - 2024 - search.proquest.com
The goal of this research is to analyze multicolor affine urn structures that evolve through
multiple drawings at each sampling stage. The jump from one to multiple balls per sample …
multiple drawings at each sampling stage. The jump from one to multiple balls per sample …
Central limit theorems for a hypergeometric randomly reinforced urn
I Crimaldi - Journal of applied probability, 2016 - cambridge.org
We consider a variant of the randomly reinforced urn where more balls can be
simultaneously drawn out and balls of different colors can be simultaneously added. More …
simultaneously drawn out and balls of different colors can be simultaneously added. More …
Strong laws for urn models with balanced replacement matrices
A Dasgupta, K Maulik - 2011 - projecteuclid.org
We consider an urn model, whose replacement matrix has all entries nonnegative and is
balanced, that is, has constant row sums. We obtain the rates of the counts of balls …
balanced, that is, has constant row sums. We obtain the rates of the counts of balls …
On affine multi-color urns grown under multiple drawing
J Sparks, M Kuba, S Balaji, H Mahmoud - arXiv preprint arXiv:2403.12423, 2024 - arxiv.org
Early investigation of P\'{o} lya urns considered drawing balls one at a time. In the last two
decades, several authors considered multiple drawing in each step, but mostly for schemes …
decades, several authors considered multiple drawing in each step, but mostly for schemes …
Strong laws for balanced triangular urns
Consider an urn model whose replacement matrix is triangular, has all nonnegative entries,
and the row sums are all equal to 1. We obtain strong laws for the counts of balls …
and the row sums are all equal to 1. We obtain strong laws for the counts of balls …