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Teor. Veroyatnost. i Primenen., 2001, Volume 46, Issue 3, Pages 483–497 (Mi tvp3897)  

This article is cited in 22 scientific papers (total in 22 papers)

On the Uniqueness in Law and the Pathwise Uniqueness for Stochastic Differential Equations

A. S. Cherny

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We prove that the uniqueness in law for an SDE
\begin{equation} dX_t^i=b_t^i(X) dt+\sum_{j=1}^m\sigma_t^{ij}(X) dB_t^j, \qquad X_0^i=x^i,\quad i=1,…,n,\quad \tag{1} \end{equation}
implies the uniqueness of the joint distribution of a pair $(X,B)$. Moreover, we prove that the uniqueness in law for (1), together with the strong existence, guarantees the pathwise uniqueness. This result is somehow “dual” to the theorem of Yamada and Watanabe.

Keywords: stochastic differential equations, weak solutions, strong solutions, uniqueness in law, pathwise uniqueness, theorem of Yamada and Watanabe.


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English version:
Theory of Probability and its Applications, 2002, 46:3, 406–419

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Received: 18.05.2001

Citation: A. S. Cherny, “On the Uniqueness in Law and the Pathwise Uniqueness for Stochastic Differential Equations”, Teor. Veroyatnost. i Primenen., 46:3 (2001), 483–497; Theory Probab. Appl., 46:3 (2002), 406–419

Citation in format AMSBIB
\by A.~S.~Cherny
\paper On the Uniqueness in Law and the Pathwise Uniqueness for Stochastic Differential Equations
\jour Teor. Veroyatnost. i Primenen.
\yr 2001
\vol 46
\issue 3
\pages 483--497
\jour Theory Probab. Appl.
\yr 2002
\vol 46
\issue 3
\pages 406--419

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