Geodesic
On events connected with reaching a~set by sample paths of a~stochastic process
Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 1, pp. 143-146

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Let $\Gamma$ be a subset in the state space of a stochastic process $x_t$. Let $I$ be an interval on the real line $T$, and $D(I)$ be the event $\{x_t\in\Gamma\ \text{at some}\ t\in I\}$. Such a system of events $D(I)$ satisfies conditions 1.A–1.B. Under some assumptions, in the Markov case, all such systems are described. The main result is applied to the analysis of a special $\sigma$-field in the space $T\times\Omega$. 
@article{TVP_1976_21_1_a11,
     author = {M. I. Taksar},
     title = {On events connected with reaching a~set by sample paths of a~stochastic process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {143--146},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_1_a11/}
}
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M. I. Taksar. On events connected with reaching a~set by sample paths of a~stochastic process. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 1, pp. 143-146. http://geodesic.mathdoc.fr/item/TVP_1976_21_1_a11/