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Teoriya Veroyatnostei i ee Primeneniya, 1980, Volume 25, Issue 4, Pages 675–682
(Mi tvp1224)
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This article is cited in 2 scientific papers (total in 2 papers)
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 $\xi_\theta(t)$.
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
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