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Processes with new better than used first-passage times
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- Journal:
- Advances in Applied Probability / Volume 16 / Issue 3 / September 1984
- Published online by Cambridge University Press:
- 01 July 2016, pp. 667-686
- Print publication:
- September 1984
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- Article
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Let
with Z(0) = 0 be a random process under investigation and N be a point process associated with Z. Both Z and N are defined on the same probability space. Let 
with R0 = 0 denote the consecutive positions of points of N on the half-line 
. In this paper we present sufficient conditions under which (Z, R) is a new better than used (NBU) process and give several examples of NBU processes satisfying these conditions. In particular we consider the processes in which N is a renewal and a general point process. The NBU property of some semi-Markov processes is also presented.
with 
with 
. In this paper we present sufficient conditions under which (