Geodesic
Discontinuous Markov Processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 3 (1958) no. 1, pp. 41-60

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A Markov process $x(t,w),t\geq0,\omega\in\Omega$, on a measurable space $(\mathscr E,\mathfrak B)$ is called a discontinuous process, if for every $\omega\in\Omega$ and $t\geq0$ there exists an $\varepsilon>0$ such that $x(t,\omega)=x(t+h,\omega)$ for all $h\in(0,\varepsilon]$. In this paper infinitesimal operators of all discontinuous processes are calculated. The results of these calculations imply the step-function processes described. 
@article{TVP_1958_3_1_a1,
     author = {E. B. Dynkin},
     title = {Discontinuous {Markov} {Processes}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {41--60},
     publisher = {mathdoc},
     volume = {3},
     number = {1},
     year = {1958},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1958_3_1_a1/}
}
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E. B. Dynkin. Discontinuous Markov Processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 3 (1958) no. 1, pp. 41-60. http://geodesic.mathdoc.fr/item/TVP_1958_3_1_a1/