Geodesic
To the Discord Problem for a~Jump-Like Markov Process
Sibirskij žurnal industrialʹnoj matematiki, Tome 12 (2009) no. 3, pp. 85-98.

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We obtain the structure of the optimal moment of halting (sending an “alarm” signal) and the integrodifferential equation for the risk function in the discord problem for an observed jump-like Markov process in the case that the discord point coincides with one of the jumps of the process.
Keywords: Markov process, detection
Mots-clés : discord. 
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G. I. Salov. To the Discord Problem for a~Jump-Like Markov Process. Sibirskij žurnal industrialʹnoj matematiki, Tome 12 (2009) no. 3, pp. 85-98. http://geodesic.mathdoc.fr/item/SJIM_2009_12_3_a8/

[1] Salov G. I., “Zadacha o razladke dlya skachkoobraznogo markovskogo protsessa”, Sib. zhurn. industr. matematiki, 11:1 (2008), 111–121

[2] Borovkov A. A., Teoriya veroyatnostei, Editorial URSS, M., 1999 | MR

[3] Shiryaev A. N., Veroyatnost, Nauka, M., 1989 | MR

[4] Meier P.-A., Veroyatnost i potentsialy, Mir, M., 1973

[5] Gikhman I. I., Skorokhod A. V., Vvedenie v teoriyu sluchainykh protsessov, Nauka, M., 1977 | MR

[6] Shiryaev A. N., Statisticheskii posledovatelnyi analiz, Nauka, M., 1969 | MR

[7] Shiryaev A. N., Statisticheskii posledovatelnyi analiz, Nauka, M., 1976 | MR | Zbl

[8] Salov G. I., “The disorder problem for pure jump Markov processes”, Proc. 2 IASTED Internat. Conf. Automation, Control, and Information Technology. Signal and Image Processing (June 20–24, 2005, Novosibirsk), ACTA Press, Anaheim–Calgary–Zurich, 2005, 205–209

[9] Dynkin E. B., Markovskie protsessy, Fizmatgiz, M., 1963 | MR

[10] de Sam Lazaro J., “Sur les helices du flot special sous une fonction”, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 30 (1974), 279–302 | DOI | MR | Zbl

[11] Davis M. H. A., “The representation of martingales of jump processes”, SIAM J. Control and Optimization, 14 (1976), 623–638 | DOI | MR | Zbl

[12] Gikhman I. I., Skorokhod A. V., Teoriya sluchainykh protsessov, T. 2, Nauka, M., 1973 | MR | Zbl

[13] Liptser R. Sh., Shiryaev A. N., Teoriya martingalov, Nauka, M., 1986 | MR | Zbl

[14] Gikhman I. I., Skorokhod A. V., Yadrenko M. I., Teoriya veroyatnostei i matematicheskaya statistika, Vischa shk., Kiev, 1979