A two-disorder detection problem

• Autorzy: Krzysztof Szajowski
• Języki publikacji: EN

Abstrakty

EN

Suppose that the process $X=\{X_n,n\in\N\}$ is observed sequentially. There are two random moments of time $θ_1$ and $θ_2$, independent of X, and X is a Markov process given $θ_1$ and $θ_2$. The transition probabilities of X change for the first time at time $θ_1$ and for the second time at time $θ_2$. Our objective is to find a strategy which immediately detects the distribution changes with maximal probability based on observation of X. The corresponding problem of double optimal stopping is constructed. The optimal strategy is found and the corresponding maximal probability is calculated.

Słowa kluczowe

EN

multiple optimal stopping; disorder problem; sequential detection

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1996-1997
• Tom: 24
• Numer: 2
• Strony: 231-241

Daty

wydano

1997

otrzymano

1996-03-15

Twórcy

autor

Krzysztof Szajowski

• Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

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• M. Nikolaev (1979), Generalized sequential procedures, Lit. Mat. Sb. 19, 35-44 (in Russian).
• M. Nikolaev (1981), On an optimality criterion for a generalized sequential procedure, ibid. 21, 75-82 (in Russian).
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• K. Szajowski (1992), Optimal on-line detection of outside observations, J. Statist. Plann. Inference 30, 413-422.
• M. Yoshida (1983), Probability maximizing approach for a quickest detection problem with complicated Markov chain, J. Inform. Optim. Sci. 4, 127-145.