Geodesic
The ``disorder'' problem for a~Poisson process
Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 4, pp. 729-734

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The paper considers a Bayesian problem of detecting the “disorder” for the process $\xi(t)$. It is shown (Theorem 1) that the optimal decision rule minimizing the risk (1) is the first time at which the a posteriori probability $\pi_t$ enters the set $[\lambda/(\lambda+c),1]$. 
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     author = {L. I. Galt\v{c}huk and B. L. Razovskiǐ},
     title = {The ``disorder'' problem for {a~Poisson} process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {729--734},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_4_a14/}
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L. I. Galtčhuk; B. L. Razovskiǐ. The ``disorder'' problem for a~Poisson process. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 4, pp. 729-734. http://geodesic.mathdoc.fr/item/TVP_1971_16_4_a14/