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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