Dr. Enrico Au-Yeung
Initially, an urn contains 3 blue balls and 1 red ball. A ball is randomly chosen from the urn. The ball is returned to the urn, together with one additional ball of the same type (red or blue). When the urn has twenty balls in it, what is the probability that exactly ten balls are blue? This is a model for a random process. This urn model has been extended in various ways and we consider some of these generalizations. Urn models can be formulated as random walks in the quarter plane. Our findings indicate that for a specific type of random walk, we can calculate the generating function explicitly. Instead of using Markov chains, our approach is to use analytical techniques from differential equations.
Bali, Harshita and Au-Yeung, Enrico
"Random Walks in the Quarter Plane: Solvable Models with an Analytical Approach,"
DePaul Discoveries: Vol. 11:
1, Article 7.
Available at: https://via.library.depaul.edu/depaul-disc/vol11/iss1/7