A Gaussian Process Approximation for a two-color Randomly Reinforced Urns

Abstract

We prove a Gaussian process approximation for the sequence of random compositions of a two-color randomly reinforced urn for both the cases with the equal and unequal reinforcement means. By using the Gaussian approximation, the law of the iterated logarithm and the functional limit central limit theorem in both the stable convergence sense and the almost-sure conditional convergence sense are established. Also as a consequence, we are able to to prove that the distribution of the urn composition has no points masses both when the reinforcement means are equal and unequal under the assumption of only finite $(2+\epsilon )$-th moments.

References in corpus (6)

• Asymptotic theorems of sequential estimation-adjusted urn models
• Asymptotics in response-adaptive designs generated by a two-color, randomly reinforced urn
• Limit distributions for large Pólya urns
• Immigrated urn models - asymptotic properties and applications
• A Central Limit Theorem, and related results, for a two-color randomly reinforced urn
• The Gaussian approximation for multi-color generalized Friedman's urn model

Cited by in corpus (3)

• Synchronization of Reinforced Stochastic Processes with a Network-based Interaction
• Interacting reinforced stochastic processes: statistical inference based on the weighted empirical means
• Networks of reinforced stochastic processes: asymptotics for the empirical means