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## Applicationes Mathematicae

1996-1997 | 24 | 2 | 231-241
Tytuł artykułu

### A two-disorder detection problem

Autorzy
Treść / Zawartość
Warianty tytułu
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
Czasopismo
Rocznik
Tom
Numer
Strony
231-241
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-03-15
Twórcy
autor
• Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Bibliografia
• T. Bojdecki (1979), Probability maximizing approach to optimal stopping and its application to a disorder problem, Stochastics 3, 61-71.
• T. Bojdecki (1982), Probability maximizing method in problems of sequential analysis, Mat. Stos. 21, 5-37 (in Polish).
• Y. Chow, H. Robbins and D. Siegmund (1971), Great Expectations: The Theory of Optimal Stopping, Houghton Mifflin, Boston.
• G. Haggstrom (1967), Optimal sequential procedures when more than one stop is required, Ann. Math. Statist. 38, 1618-1626.
• 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).
• A. Shiryaev (1978), Optimal Stopping Rules, Springer, New York.
• 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.
Typ dokumentu
Bibliografia
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