Abstract
Let Xi,i ∈ ℕ, be independent and identically distributed random variables with values in ℕ0. We transform (`prune') the sequence {X1,...,Xn},n∈ ℕ, of discrete random samples into a sequence {0,1,2,...,Yn}, n∈ ℕ, of contiguous random sets by replacing Xn+1 with Yn +1 if Xn+1 >Yn. We consider the asymptotic behaviour of Yn as n→∞. Applications include path growth in digital search trees and the number of tables in Pitman's Chinese restaurant process if the latter is conditioned on its limit value.
Citation
Rudolf Grübel. Paweł Hitczenko. "Pruned discrete random samples." J. Appl. Probab. 50 (2) 542 - 556, June 2013. https://doi.org/10.1239/jap/1371648960
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