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Limit laws for a sequence between the maximum and the sum of independent exponentials

✍ Scribed by João Gomes; Orlando Oliveira

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
279 KB
Volume
35
Category
Article
ISSN
0167-7152

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✦ Synopsis

Consider a stochastic process {X.}, n = 0, 1, 2 .... with initial value Xo and a sequence of independent, random variables, { Yi}, i ~ N with exponential distribution with parameter one, where X. + 1 = max(X., aX. + Y. + t), 0 < a < 1. In this paper, we show that this sequence behaves like the sequence of maxima as far as record values are concerned, that {X. -I-Log(n)]/[1 -~]} converges weakly to a nondegenerate random variable Z and, finally, we show that (1 -~)X. q.¢.

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