Unbalanced urn model with random addition

TL;DR

This paper introduces a multi-drawing urn model with random addition, analyzing its long-term behavior using stochastic approximation, and providing limit theorems for the proportion of white balls.

Contribution

It presents a novel multi-drawing urn model with random addition and derives asymptotic results using stochastic approximation techniques.

Findings

Asymptotic behavior of white balls characterized

Limit theorems established for the urn model

Model incorporates random variables with finite means and variances

Abstract

In this paper, we consider a multi-drawing urn model with random addition. At each discrete time step, we draw a sample of m balls. According to the composition of the drawn colors, we return the balls together with a random number of balls depending on two discrete random variables X and Y with finite means and variances. Via the stochastic approximation algorithm, we give limit theorems describing the asymptotic behavior of white balls.