Unbalanced multi-drawing urn with random addition matrix. Issue 1 (11th January 2019)

• Record Type: Journal Article
• Authors: Rafik, Aguech; Olfa, Selmi
• Is Part Of: Arab journal of mathematical sciences. Volume 26:Issue 1/2(2020)
• Page Start: 57
• Page End: 74
• Publication Date: 2019-01-11
• Subjects: Central limit theorem -- Unbalanced urn -- Martingale -- Stochastic algorithm
• DOI: 10.1016/j.ajmsc.2018.12.004
• Languages: English
• ISSNs: 1319-5166

Abstract

Abstract : In this paper, we consider a two color multi-drawing urn model. At each discrete time step, we draw uniformly at random a sample of m balls ( m ≥ 1 ) and note their color, they will be returned to the urn together with a random number of balls depending on the sample's composition. The replacement rule is a 2 × 2 matrix depending on bounded discrete positive random variables. Using a stochastic approximation algorithm and martingales methods, we investigate the asymptotic behavior of the urn after many draws.