Geodesic
On Conditional Markov Processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 5 (1960) no. 2, pp. 227-228

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In this paper a pair of random processes $X_t$, $Y_t$, which conjunctly form the Markov process $Z_t$ is considered. The conditional distribution of the process $Y_t$ for the condition of a known realization of the process $X_t$ during some time interval is examined. E. B. Dynkin has proposed that if $X_t$ is a Markov process, the conditional distribution of $Y_t$ will satisfy a functional equation similar to the known Kolmogorov–Chapman equation. The author has proved this proposition, but details of the proof are omitted here. 
@article{TVP_1960_5_2_a5,
     author = {C. S. Leung},
     title = {On {Conditional} {Markov} {Processes}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {227--228},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {1960},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1960_5_2_a5/}
}
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C. S. Leung. On Conditional Markov Processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 5 (1960) no. 2, pp. 227-228. http://geodesic.mathdoc.fr/item/TVP_1960_5_2_a5/