Geodesic
Conditional Markov Processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 5 (1960) no. 2, pp. 172-195

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Relationships are given between the probabilities of conditional Markov chains for neighboring tests. The conditional probabilities at the end of the observation interval (the final probabilities) are satisfied by equations of the first kind corresponding to an increase in the observation interval. The equations of the second kind for the conditional probabilities within the observation interval are written in terms of these final probabilities. The following special cases are considered. Gaussian noise with independent values which becomes a delta-correlational process when the moments of time are compacted, and a continuous Markov process. The related problem of the time reversal of ordinary (a priori) Markov processes is treated as a side issue. 
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     author = {R. L. Stratonovich},
     title = {Conditional {Markov} {Processes}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {172--195},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {1960},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1960_5_2_a1/}
}
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R. L. Stratonovich. Conditional Markov Processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 5 (1960) no. 2, pp. 172-195. http://geodesic.mathdoc.fr/item/TVP_1960_5_2_a1/