We construct a response adaptive design, described in terms of a two-color urn model, targeting fixed asymptotic allocations. We prove asymptotic results for the process of colors generated by the urn and for the process of its compositions. An application of the proposed urn model is presented in an estimation problem context.
"Randomly reinforced urn designs with prespecified allocations." J. Appl. Probab. 50 (2) 486 - 498, June 2013. https://doi.org/10.1239/jap/1371648956