%0 Journal Article %1 gpy04 %A Gnedin, Alexander %A Pitman, Jim %A Yor, Marc %D 2006 %J Ann. Probab. %K Dept_Mathematics_Berkeley Dept_Statistics_Berkeley asymptotic_law random_compositions subordinator myown %N 2 %P 468--492 %R 0.1214/009117905000000639 %T Asymptotic laws for compositions derived from transformed subordinators %V 34 %X A random composition of $n$ appears when the points of a random closed set $\mathcalR\subset0,1$ are used to separate into blocks $n$ points sampled from the uniform distribution. We study the number of parts $K_n$ of this composition and other related functionals under the assumption that $\mathcalR=\phi(S_\bullet)$, where $(S_t,t\geq0)$ is a subordinator and $\phi:0,ınfty\to0,1$ is a diffeomorphism. We derive the asymptotics of $K_n$ when the Lévy measure of the subordinator is regularly varying at 0 with positive index. Specializing to the case of exponential function $\phi(x)=1-e^-x$, we establish a connection between the asymptotics of $K_n$ and the exponential functional of the subordinator.

@article{gpy04, abstract = {A random composition of $n$ appears when the points of a random closed set $\widetilde{\mathcal{R}}\subset[0,1]$ are used to separate into blocks $n$ points sampled from the uniform distribution. We study the number of parts $K_n$ of this composition and other related functionals under the assumption that $\widetilde{\mathcal{R}}=\phi(S_{\bullet})$, where $(S_t,t\geq0)$ is a subordinator and $\phi:[0,\infty]\to[0,1]$ is a diffeomorphism. We derive the asymptotics of $K_n$ when the L\'{e}vy measure of the subordinator is regularly varying at 0 with positive index. Specializing to the case of exponential function $\phi(x)=1-e^{-x}$, we establish a connection between the asymptotics of $K_n$ and the exponential functional of the subordinator.}, added-at = {2008-01-21T00:00:55.000+0100}, arxiv = {math.PR/0403438}, author = {Gnedin, Alexander and Pitman, Jim and Yor, Marc}, biburl = {https://www.bibsonomy.org/bibtex/2c47062e77b3418480a9322d65373ab79/pitman}, coden = {APBYAE}, doi = {0.1214/009117905000000639}, fjournal = {The Annals of Probability}, interhash = {5f3646b95a80b59eca3cdf15d408a7f6}, intrahash = {c47062e77b3418480a9322d65373ab79}, issn = {0091-1798}, journal = {Ann. Probab.}, keywords = {Dept_Mathematics_Berkeley Dept_Statistics_Berkeley asymptotic_law random_compositions subordinator myown}, mrclass = {60G09 (60C05)}, mrnumber = {MR2223948}, mrreviewer = {Martin V. Hildebrand}, number = 2, pages = {468--492}, timestamp = {2010-10-30T22:51:58.000+0200}, title = {Asymptotic laws for compositions derived from transformed subordinators}, volume = 34, year = 2006 }