The exponential rate of convergence of the distribution of the maximum of a random walk. Part II
- 1 December 1976
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 13 (4) , 733-740
- https://doi.org/10.2307/3212528
Abstract
Let Gn (x) be the distribution of the nth successive maximum of a random walk on the real line. Under conditions typical for complete exponential convergence, the decay of Gn (x) – limn→∞ Gn(x) is asymptotically equal to H(x) γn n–3/2 as n → ∞where γ < 1 and H(x) a function solely depending on x. For the case of drift to + ∞, G∞(x) = 0 and the result is new; for drift to – ∞we give a new proof, simplifying and correcting an earlier version in [9].Keywords
This publication has 6 references indexed in Scilit:
- The exponential rate of convergence of the distribution of the maximum of a random walkJournal of Applied Probability, 1975
- Random walks with negative drift conditioned to stay positiveJournal of Applied Probability, 1974
- Complete exponential convergence and some related topicsJournal of Applied Probability, 1967
- Geometric ergodicity in a class of denumerable Markov chainsProbability Theory and Related Fields, 1966
- On the Probabilities of Large Deviations for Sums of Independent Random VariablesTheory of Probability and Its Applications, 1965
- On Deviations of the Sample MeanThe Annals of Mathematical Statistics, 1960