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Some martingales related to cumulative sum tests and single-server queues. (English) Zbl 0338.60030

MSC:
60J65 Brownian motion
60G50 Sums of independent random variables; random walks
60K25 Queueing theory (aspects of probability theory)
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[1] Brockwell, P.J., Deviations from monotonicity of a Wiener process with drift, J. appl. probability, 11, 206-210, (1974) · Zbl 0275.60086
[2] van Dobben de Bruyn, D.S., Cumulative sum tests: theory and practice, (1968), Griffin London
[3] Freedman, D., Brownian motion and diffusion, (1971), Holden-Day San Francisco · Zbl 0231.60072
[4] Johnson, R.A.; Bagshaw, M., The effect of serial correlation on the performance of CUSUM tests, Technometrics, 16, 103-112, (1974) · Zbl 0277.62069
[5] Prabhu, N.U., Queues and inventories, (1965), John Wiley New York · Zbl 0131.16904
[6] Takacs, L., Combinatorial methods in the theory of stochastic processes, (1967), John Wiley New York · Zbl 0189.17602
[7] Taylor, H.M., A stopped Brownian motion formula, Ann. probability, 3, 234-246, (1975) · Zbl 0303.60072
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