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Weak convergence and first passage times

Published online by Cambridge University Press:  14 July 2016

Allan Gut
Allan Gut*
Affiliation:
University of Uppsala
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Abstract

Let Sn, n = 1, 2, ‥, denote the partial sums of i.i.d. random variables with the common distribution function F and positive, finite mean. Let N(c) = min [k; Sk > c‥kp], c ≥ 0, 0 ≤ p < 1. Under the assumption that F belongs to the domain of attraction of a stable law with index α, 1 < α ≤ 2, functional central limit theorems for the first passage time process N(nt), 0 ≤ t ≤ 1, when n → ∞, are derived in the function space D[0,1].

Keywords

WEAK CONVERGENCEFIRST PASSAGE TIMESKOROHOD J1-TOPOLOGYSKOROHOD M1-TOPOLOGYSUPREMUM FUNCTIONFIRST PASSAGE TIME FUNCTIONCONTINUOUS MAPPING THEOREMRANDOM CHANGE OF TIME
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 2 , June 1975 , pp. 324 - 332
Copyright
Copyright © Applied Probability Trust 1975 

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