Geodesic
Families of Consistent Probability Measures
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 1, pp. 160-163

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This paper deals with the following problem. Suppose that $(P_t)_{t\ge 0}$ is a family of consistent probability measures defined on a filtration $(\mathscr{F}_t)_{t\ge 0}$. Does there exist a measure $P$ on the $\sigma$-field $\vee_{t\geq 0}\mathscr{F}_t$ such that $P\,|\,\mathscr{F}_t=P_t$? The answer is positive for the spaces $C(\mathbf{R}_+,\mathbf{R}^d)$ and $D(\mathbf{R}_+,\mathbf{R}^d)$ endowed with the natural filtration. We prove this statement using a simple method based on the Prokhorov criterion of weak compactness.
Keywords: consistent probability measures, extension of measures, Skorokhod space, Prokhorov criterion. 
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     author = {A. S. Cherny},
     title = {Families of {Consistent} {Probability} {Measures}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_1_a10/}
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A. S. Cherny. Families of Consistent Probability Measures. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 1, pp. 160-163. http://geodesic.mathdoc.fr/item/TVP_2001_46_1_a10/