Lectures on
Probability and Stochastic Processes IX

Indian Statistical Institute, Kolkata
December 12 - 16, 2014

Urn Schemes with Negative Reinforcement

Gursharn Kaur

In this work we consider negatively reinforced Polya type urn processes with finitely many colors. We consider two types of such processes Linear and Inverse. We show that in case of only two colors both the processes are equivalent and the limiting configuration of the urn is uniform a.s., and for more than two color case the configuration of the urn after $n$ draws converge a.s. to a limiting distribution which is uniform if and only if uniform distribution is the unique stationary distribution of the underlying Markov chain.