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

V. V. Vysotsky

doi:10.1007/s10958-007-0510-x

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

V. V. Vysotsky

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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)
Pages (from-to)	6873-6883
Number of pages	11
Journal	Journal of Mathematical Sciences
Volume	147
Issue number	4
DOIs	https://doi.org/10.1007/s10958-007-0510-x
State	Published - Dec 2007
Externally published	Yes

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Applied Mathematics

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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.",

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

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