Geodesic
On extensions of a Markov process
Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 4, pp. 708-713 
E. B. Dynkin. On extensions of a Markov process. Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 4, pp. 708-713. http://geodesic.mathdoc.fr/item/TVP_1968_13_4_a9/
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     author = {E. B. Dynkin},
     title = {On extensions of {a~Markov} process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {708--713},
     year = {1968},
     volume = {13},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1968_13_4_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $D$ be an open set in a compact metric space $E$. A Markov process $X$ in $E$ is called an extension of a process $X^0$ given in $D$, if the part of $X$ on $D$ is equivalent to $X^0$. In this paper characteristics are introduced which describe extensions $X$ of a process $X^0$. An analogous problem was recently treated by Motoo [4]. We investigate the problem by other methods and under more general conditions.