The exponential rate of convergence of the distribution of the maximum of a random walk
- 1 June 1975
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 12 (2) , 279-288
- https://doi.org/10.2307/3212441
Abstract
Let Gn(x) be the distribution function of the maximum of the successive partial sums of independent and identically distributed random variables and G(x) its limiting distribution function. Under conditions, typical for complete exponential convergence, the decay of Gn(x) — G(x) is asymptotically equal to c.H(x)n−3/2γn as n → ∞ where c and γ are known constants and H(x) is a function solely depending on x.Keywords
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This publication has 2 references indexed in Scilit:
- Limit theorems in fluctuation theoryAdvances in Applied Probability, 1973
- Complete exponential convergence and some related topicsJournal of Applied Probability, 1967