On a~characterization of certain families of measures
Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 1, pp. 134-136
Voir la notice de l'article provenant de la source Math-Net.Ru
Let $(\xi_t)$, $t\in[0,1]$, be a measurable stochastic process. Put
$$
\mu_t(A)=\int_0^t 1_A(\xi_s)\,ds\qquad A\in\mathscr B,
$$
where $\mathscr B$ is the Borel $\sigma$-algebra in $R^1$. It is easy to see that the family has the following two properties:
1) for any $A\in\mathscr B$ the function $t\rightsquigarrow\mu_t(A)$ is non-decreasing;
2) for any $t\in[0,1]$, $\mu_t(R^1)=t$.
We give a characterization of families $(\mu_t)$, with properties 1) and 2), which are generated by a stochastic process.
@article{TVP_1978_23_1_a9,
author = {Yu. A. Davydov and A. L. Rozin},
title = {On a~characterization of certain families of measures},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {134--136},
publisher = {mathdoc},
volume = {23},
number = {1},
year = {1978},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1978_23_1_a9/}
}
Yu. A. Davydov; A. L. Rozin. On a~characterization of certain families of measures. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 1, pp. 134-136. http://geodesic.mathdoc.fr/item/TVP_1978_23_1_a9/