Urn models with random multiple drawing and random addition

Abstract

We consider an urn model with multiple drawing and random time-dependent addition matrix. The model is very general with respect to previous literature: the number of sampled balls at each time-step is random, the addition matrix has general random entries. For the proportion of balls of a given color, we prove almost sure convergence results and fluctuation theorems (through CLTs in the sense of stable convergence and of almost sure conditional convergence, which are stronger than convergence in distribution). Asymptotic confidence intervals are given for the limit proportion, whose distribution is generally unknown.

References in corpus (6)

• Epidemic processes in complex networks
• A survey of random processes with reinforcement
• Asymptotics in response-adaptive designs generated by a two-color, randomly reinforced urn
• Central limit theorems for an Indian buffet model with random weights
• Urns with simultaneous drawing
• Classification of urn models with multiple drawings