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Teor. Veroyatnost. i Primenen., 1980, Volume 25, Issue 4, Pages 675–682 (Mi tvp1224)  

Stochastic differential equations depending on a parameter

A. V. Skorohod

Kiev

Abstract: We consider a stochastic differential equation
$$ d\xi_\theta=a_\theta(t,\xi_\theta( \cdot )) dt+B_\theta(t,\xi_\theta(t)) dw(t),\qquad\xi_\theta(0)=x_\theta, $$
such that its coefficients and initial condition are continuous functions of $\theta\in\Theta$, where $\Theta$ is a complete metric space. If an equation has a strong solution on a dense subset $\Theta_1\subset\Theta$, then $\Theta_1$ is of the second category and coincides with the set $\Theta_0$ of continuity of $\xi_\theta(t)$.

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English version:
Theory of Probability and its Applications, 1981, 25:4, 659–666

Bibliographic databases:

Received: 04.07.1979

Citation: A. V. Skorohod, “Stochastic differential equations depending on a parameter”, Teor. Veroyatnost. i Primenen., 25:4 (1980), 675–682; Theory Probab. Appl., 25:4 (1981), 659–666

Citation in format AMSBIB
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\by A.~V.~Skorohod
\paper Stochastic differential equations depending on a~parameter
\jour Teor. Veroyatnost. i Primenen.
\yr 1980
\vol 25
\issue 4
\pages 675--682
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=595131}
\zmath{https://zbmath.org/?q=an:0471.60067|0454.60058}
\transl
\jour Theory Probab. Appl.
\yr 1981
\vol 25
\issue 4
\pages 659--666
\crossref{https://doi.org/10.1137/1125083}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980MK50200001}


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