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A Gaussian Process Approximation for a two-color Randomly Reinforced Urns
We prove a Gaussian process approximation for the sequence of random
compositions of a two-color randomly reinforced urn for both the cases with the
equal and unequal reinforcement means. By using the Gaussian approximation, the
law of the iterated logarithm and the functional limit central limit theorem in
both the stable convergence sense and the almost-sure conditional convergence
sense are established. Also as a consequence, we are able to to prove that the
distribution of the urn composition has no points masses both when the
reinforcement means are equal and unequal under the assumption of only finite
-th moments
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