Analysis of a Class of Cannibal Urns
نویسنده
چکیده
In this note we study a class of 2× 2 Pólya-Eggenberger urn models, with ball transition matrix given by M = ( 0 −b c −d ) , for arbitrary parameters b, c ∈ N, assuming the balancing condition d = c+ b. This urn model serves as a stochastic model in biology describing cannibalistic behavior of populations. The special case b = c = 1 and d = 2 was studied by Pittel [16] using asymptotic approximation techniques, and more recently by Hwang et al. [10] using generating functions. We obtain limit laws for the stated class of cannibal urns by using Pittel’s method, and also different techniques.
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