### Abstract

Let S_{i} be a random walk with standard exponential increments. The sum ∑_{i=1} ^{k} S_{i} is called the k-step area of the walk. The random variable _{k≥1} 2/k(k + 1)} ∑ _{i=1} ^{k} S_{i} plays an important role in the study of the so-called one-dimensional sticky particles model. We find the distribution of this variable and prove that Equation Presented We also show that Equation Presented, where the U_{i,n} are order statistics of n i.i.d. random variables uniformly distributed on [0, 1]. Bibliography: 6 titles.

Original language | English (US) |
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Pages (from-to) | 6873-6883 |

Number of pages | 11 |

Journal | Journal of Mathematical Sciences |

Volume | 147 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2007 |

### ASJC Scopus subject areas

- Statistics and Probability
- Mathematics(all)
- Applied Mathematics

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## Cite this

Vysotsky, V. V. (2007). The area of an exponential random walk and partial sums of uniform order statistics.

*Journal of Mathematical Sciences*,*147*(4), 6873-6883. https://doi.org/10.1007/s10958-007-0510-x