کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5130035 | 1378654 | 2017 | 28 صفحه PDF | دانلود رایگان |

For a given random sequence (C,T1,T2,â¦), the smoothing transform S maps the law of a real random variable X to the law of âkâ¥1TkXk+C, where X1,X2,⦠are independent copies of X and also independent of (C,T1,T2,â¦). This law is a fixed point of S if X=dâkâ¥1TkXk+C holds true, where =d denotes equality in law. Under suitable conditions including EC=0, S possesses a unique fixed point within the class of centered distributions, called the canonical solution because it can be obtained as a certain martingale limit in an associated weighted branching model. The present work provides conditions on (C,T1,T2,â¦) such that the canonical solution exhibits right and/or left Poissonian tails and the abscissa of convergence of its moment generating function can be determined. As a particular application, the right tail behavior of the Quicksort distribution is found.
Journal: Stochastic Processes and their Applications - Volume 127, Issue 9, September 2017, Pages 3014-3041