Geodesic
On sets of laws of continuous martingales
Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 4, pp. 823-828

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We prove that the set of laws of stochastic integrals $H\,{\cdot}\, W$, where $W$ is a multidimensional Wiener process and $H^2$ takes values in a compact convex subset $\mathbf{D}$ of the set of symmetric positive semidefinite matrices, is weakly dense in the set of laws of martingales $M$ with $d\langle M \rangle/dt$ taking values in $\mathbf{D}$.
Keywords: Wiener process, continuous martingales, stochastic integrals, weak convergence of measures. 
@article{TVP_2020_65_4_a9,
     author = {Yu. M. Kabanov},
     title = {On sets of laws of continuous martingales},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {823--828},
     publisher = {mathdoc},
     volume = {65},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2020_65_4_a9/}
}
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Yu. M. Kabanov. On sets of laws of continuous martingales. Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 4, pp. 823-828. http://geodesic.mathdoc.fr/item/TVP_2020_65_4_a9/