# A two-disorder detection problem

Applicationes Mathematicae (1997)

- Volume: 24, Issue: 2, page 231-241
- ISSN: 1233-7234

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topSzajowski, Krzysztof. "A two-disorder detection problem." Applicationes Mathematicae 24.2 (1997): 231-241. <http://eudml.org/doc/219165>.

@article{Szajowski1997,

abstract = {Suppose that the process $X=\lbrace X_n,n\in \mathbb \{N\}\rbrace $ 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.},

author = {Szajowski, Krzysztof},

journal = {Applicationes Mathematicae},

keywords = {multiple optimal stopping; disorder problem; sequential detection},

language = {eng},

number = {2},

pages = {231-241},

title = {A two-disorder detection problem},

url = {http://eudml.org/doc/219165},

volume = {24},

year = {1997},

}

TY - JOUR

AU - Szajowski, Krzysztof

TI - A two-disorder detection problem

JO - Applicationes Mathematicae

PY - 1997

VL - 24

IS - 2

SP - 231

EP - 241

AB - Suppose that the process $X=\lbrace X_n,n\in \mathbb {N}\rbrace $ 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.

LA - eng

KW - multiple optimal stopping; disorder problem; sequential detection

UR - http://eudml.org/doc/219165

ER -

## References

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- Y. Chow, H. Robbins and D. Siegmund (1971), Great Expectations: The Theory of Optimal Stopping, Houghton Mifflin, Boston. Zbl0233.60044
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- 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. Zbl0391.60002
- K. Szajowski (1992), Optimal on-line detection of outside observations, J. Statist. Plann. Inference 30, 413-422. Zbl0752.60034
- M. Yoshida (1983), Probability maximizing approach for a quickest detection problem with complicated Markov chain, J. Inform. Optim. Sci. 4, 127-145. Zbl0511.60041

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