Abstract
1. At the outset we will assume that with the original probabilistic-statistical experiment \((\Omega ,\mathcal {F}, (\mathcal {F}_t)_{t \geqslant 0};\mathrm {P}^{\kern 1pt 0}, \mathrm {P}^{\infty })\), where
there are associated “θ-models” and “G-models” (Sects. 1.2 and 1.3).
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Notes
- 1.
By definition, for any random variable X(ω), given on a probability space \((\Omega , \mathcal {F},\mathrm {P})\), \({\mathrm {ess}\,\mathrm {sup}}_\omega X(\omega )=\inf \{C\colon \mathrm {P} (X(\omega ) \leqslant C)=1\}\).
- 2.
The statistics ψ n, \(n \geqslant 1\), known as the Shiryaev–Roberts statistics, will play an important role in the sequel (for instance, in variant B).
- 3.
CUSUM is short for CUmulative SUM.
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Shiryaev, A.N. (2019). Basic Settings and Solutions of Quickest Detection Problems. Discrete Time. In: Stochastic Disorder Problems. Probability Theory and Stochastic Modelling, vol 93. Springer, Cham. https://doi.org/10.1007/978-3-030-01526-8_2
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