An extended Polya urn Model with two colors, black and white, is studied with some SLLN and CLT on the proportion of white balls.
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.
