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Locally best tests for Gaussian processes. (English) Zbl 0429.62059

MSC:
62L10 Sequential statistical analysis
60G15 Gaussian processes
62M02 Markov processes: hypothesis testing
62L15 Optimal stopping in statistics
60G40 Stopping times; optimal stopping problems; gambling theory
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References:
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[2] Berk, R.H.: Locally most powerful tests. Ann. Stat.3, 1975, 373–381. · Zbl 0332.62063 · doi:10.1214/aos/1176343063
[3] Bhattacharya, P.K., andR.P. Smith: Sequential probability ratio test for the mean value function of a Gaussian process. Ann. Math. Stat.43, 1972, 1861–1873. · Zbl 0263.62048 · doi:10.1214/aoms/1177690857
[4] Darling, D.A., andA.J. Siegert: The first passage problem for a continuous Markov process. Ann. Math. Stat.24, 1953, 624–639. · Zbl 0053.27301 · doi:10.1214/aoms/1177728918
[5] Freedman, D.: Brownian Motion and Diffusion. San Francisco 1971. · Zbl 0231.60072
[6] Gihman, I.I., andA.V. Skorohod: Stochastic Differential Equations. Berlin 1972. · Zbl 0242.60003
[7] Meschkowski, H.: Hilbertsche Räume mit Kernfunktionen. Berlin 1962. · Zbl 0103.08802
[8] Parthasarathy, K.R.: Probability Measures on Metric Spaces. New York 1967. · Zbl 0153.19101
[9] Parzen, E.: Statistical analysis on time series by Hilbert space methodsI, 1959. Time Series Analysis Papers, by E. Parzen. San Francisco 1967.
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