The threshold probability for unoriented site percolation is such that
\begin{eqnarray*} \mathbb{P}_{p} & = & \underset{v\in\mathbb{\mathbb{L}}^{d}}{\prod}\mu_{v}\\ \theta(p) & = & \mathbb{P}_{p}(\mid C\mid=\infty)\\ p_{c} & = & \text{sup}\{p\mid\theta(p)=0\} \end{eqnarray*}
as given by Wolfram. I cannot find similar definitions for oriented site percolation such as here. So
How is the oriented threshold probability defined for oriented site percolation?