Moments of balanced Pólya urns

2025/05/20 by Svante Janson, Janson, Svante
Mathematics · #60C05 #60F25 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2505.14198

openalex publication_date 2025/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give bounds for (central) moments for balanced Pólya 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 previously known results, but are here given more generally and with a simpler proof.

Citations

• Almost sure and moment convergence for triangular Pólya urns
• Moment convergence of balanced Pólya processes
• Mean and variance of balanced Pólya urns
• Asymptotics in randomized urn models
• Functional limit theorems for multitype branching processes and generalized Pólya urns
• Embedding of Urn Schemes into Continuous Time Markov Branching Processes and Related Limit Theorems

Related

• Moment convergence of balanced Pólya processes
• Mean and variance of balanced Pólya urns
• Almost sure and moment convergence for triangular Pólya urns
• A Central Limit Theorem and its Applications to Multicolor Randomly Reinforced Urns
• Characterizations of asymptotic distributions of continuous-time Pólya processes