Concepedia

The Asymptotic Distribution of the Range of Sums of Independent Random Variables

The Annals of Mathematical Statistics · 1951 · 548 citations · 3 references

Open access

Concepts

Natural SciencesMathematicsProbability TheoryStatisticsStochastic ProcessesBrownian MotionMarkov ProcessesProbability DistributionsAsymptotic AnalysisAsymptotic Distribution TheoryAsymptotic TheoryBrownian Motion AnalysisBrownian Motion ApproximationsIndependent VariablesStandard Brownian MotionSums Of Random Variables

Abstract

The asymptotic distribution of the range and normalized range of the sum of $n$ independent variables is derived using the theory of Brownian motion.

References

3

An introduction to probability theory and its applications

Journal of the Franklin Institute · 1958 · 30K citations

Natural Sciences, Mathematics, Probability Theory +11

Long-Term Storage Capacity of Reservoirs

H. E. Hurst · Transactions of the American Society of Civil Engineers · 1951 · 6.2K citations

Engineering, Hydrology, Petroleum Engineering +15

Heuristic Approach to the Kolmogorov-Smirnov Theorems

J. L. Doob · The Annals of Mathematical Statistics · 1949 · 519 citations · Full text

Natural Sciences, Mathematics, Physics +13