Let $\mathscr{X}$ be a dlt model of $\mathscr{X}$, with special fiber $\mathscr{X}_{k}=\sum_{i\in I}a_{i}D_{i}$. Let $J\subset I$ such that $D_{J}=\cap_{j\in J}D_{j}$ is non-empty, and $Y$ a connected component of $D_{J}$, with generic point $\eta$. We furthermore fix a local equation $z_{j}\in\mathcal{O}_{\mathscr{X},\eta}$ for $D_{j}$, for any $j\in J$.
Then, for any $w\in\tau_{Y}=\{w\in\mathbb{R}^{|J|}_{\geqslant 0}\,|\sum_{j\in J}a_{j}w_{j}=1\}$, there exists a unique valuation

$$v_{w}:\mathcal{O}_{\mathscr{X},\eta}\longrightarrow\mathbb{R}_{\geqslant 0}\cup\{+\infty\}$$

such that for every $f\in\mathcal{O}_{\mathscr{X},\eta}$, with expansion $f=\sum_{\beta\in\mathbb{N}^{|J|}}c_{\beta}z^{\beta}$ (with $c_{\beta}$ either zero or unit), we have:

$$v_{w}(f)=\min\{(w\cdot\beta)\,|\beta\in\mathbb{N}^{|J|},c_{\beta}\neq 0\},$$

where $(\;\cdot\;)$ is the usual scalar product on $\mathbb{R}^{|J|}$.