The area of exponential random walk and partial sums of uniform order statistics
| dc.creator | Vysotsky, Vladislav | |
| dc.date | 2006-12-17 | |
| dc.date | 2007-05-14 | |
| dc.date.accessioned | 2026-07-07T08:01:05Z | |
| dc.date.available | 2026-07-07T08:01:05Z | |
| dc.description | Let S_i be a random walk with standard exponential increments. We call \sum_{i=1}^k S_i its k-step area. The random variable V = \inf_{k \ge 1} \frac{2}{k(k+1)} \sum_{i=1}^k S_i plays important role in the study of so-called one-dimensional sticky particles model. We find the distribution of V and prove that P(V > t) = \sqrt{1-t} exp(-t/2) for t in [0,1]. We also show that the variables \min_{1 \le k \le n} \frac{2n}{k(k+1)} \sum_{i=1}^k U_{i, n} converge in distribution to V. Here U_{i, n} are the order statistics of n i.i.d. random variables uniformly distributed on [0,1]. | |
| dc.description | Added one reference; corrected few typos; added one sentence to Proposition 1 | |
| dc.identifier | https://arxiv.org/abs/math/0612490 | |
| dc.identifier | http://arxiv.org/abs/math/0612490 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128839 | |
| dc.subject | Probability | |
| dc.subject | 60G50 (primary), 62G30 (secondary) | |
| dc.title | The area of exponential random walk and partial sums of uniform order statistics | |
| dc.type | text |