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Convergence of Some Expected First Passage Times
- Source :
- Ann. Probab. 4, no. 6 (1976), 1027-1029
- Publication Year :
- 1976
- Publisher :
- The Institute of Mathematical Statistics, 1976.
-
Abstract
- We discuss the convergence of the expected times until the partial sums of a sequence of independent, identically distributed random variables with zero means and unit variances first rise a height $h$ above their previous minimum as $h \rightarrow \infty$. We also consider the convergence as $r \rightarrow \infty$ of the expected times until the range of these partial sums exceeds a value $r$. Applications of these results to a quality control procedure and to queueing theory are mentioned.
- Subjects :
- Statistics and Probability
Mathematical optimization
60G50
Average run length
average run length
detecting a change in a parameter
Expected first passage times
Wiener process
symbols.namesake
60K25
Convergence (routing)
range of partial sums
symbols
62N10
Applied mathematics
Statistics, Probability and Uncertainty
60F99
Mathematics
maximum waiting time
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Ann. Probab. 4, no. 6 (1976), 1027-1029
- Accession number :
- edsair.doi.dedup.....cc5be6c126ccf9160e3cf62e42d15538