Abstract
A random composition of n appears when the points of a random closed set ℛ̃⊂[0,1] are used to separate into blocks n points sampled from the uniform distribution. We study the number of parts Kn of this composition and other related functionals under the assumption that ℛ̃=ϕ(S•), where (St,t≥0) is a subordinator and ϕ:[0,∞]→[0,1] is a diffeomorphism. We derive the asymptotics of Kn when the Lévy measure of the subordinator is regularly varying at 0 with positive index. Specializing to the case of exponential function ϕ(x)=1−e−x, we establish a connection between the asymptotics of Kn and the exponential functional of the subordinator.
Citation
Alexander Gnedin. Jim Pitman. Marc Yor. "Asymptotic laws for compositions derived from transformed subordinators." Ann. Probab. 34 (2) 468 - 492, March 2006. https://doi.org/10.1214/009117905000000639
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