The area of an exponential random walk and partial sums of uniform order statistics

V. V. Vysotsky

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Let Si be a random walk with standard exponential increments. The sum ∑i=1 k Si is called the k-step area of the walk. The random variable k≥1 2/k(k + 1)} ∑ i=1 k Si 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 Ui,n are order statistics of n i.i.d. random variables uniformly distributed on [0, 1]. Bibliography: 6 titles.

Original languageEnglish (US)
Pages (from-to)6873-6883
Number of pages11
JournalJournal of Mathematical Sciences
Volume147
Issue number4
DOIs
StatePublished - Dec 1 2007

ASJC Scopus subject areas

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

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