Geodesic
On optimal stopping rules for stochastic processes with continuous parameter
Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 2, pp. 336-344

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The main result of this note is the proof of the existence of optimal (may be, unbounded) stopping times for a process with continuous parameter. The optimal stopping rules and the corresponding maximal rewards are described in terms of some majorizing process (minimal right-continuous supermartingale). 
@article{TVP_1970_15_2_a14,
     author = {A. G. Fakeev},
     title = {On optimal stopping rules for stochastic processes with continuous parameter},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {336--344},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1970_15_2_a14/}
}
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A. G. Fakeev. On optimal stopping rules for stochastic processes with continuous parameter. Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 2, pp. 336-344. http://geodesic.mathdoc.fr/item/TVP_1970_15_2_a14/