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Teoriya Veroyatnostei i ee Primeneniya, 2020, Volume 65, Issue 4, Pages 823–828
DOI: https://doi.org/10.4213/tvp5280 (Mi tvp5280) 		 
Short Communications

On sets of laws of continuous martingales

Yu. M. Kabanovabc

a Université Bourgogne Franche-Comté, Laboratoire de Mathématiques, France
b Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow
c Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/tvp5280
Abstract: 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.
Received: 07.12.2018
Revised: 31.12.2019
English version:
Theory of Probability and its Applications, 2021, Volume 65, Issue 4, Pages 652–655
DOI: https://doi.org/10.1137/S0040585X97T990198
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Yu. M. Kabanov, “On sets of laws of continuous martingales”, Teor. Veroyatnost. i Primenen., 65:4 (2020), 823–828; Theory Probab. Appl., 65:4 (2021), 652–655
Citation in format AMSBIB
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\by Yu.~M.~Kabanov
\paper On sets of laws of continuous martingales
\jour Teor. Veroyatnost. i Primenen.
\yr 2020
\vol 65
\issue 4
\pages 823--828
\mathnet{http://mi.mathnet.ru/tvp5280}
\crossref{https://doi.org/10.4213/tvp5280}
\transl
\jour Theory Probab. Appl.
\yr 2021
\vol 65
\issue 4
\pages 652--655
\crossref{https://doi.org/10.1137/S0040585X97T990198}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000616235300010}
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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