  Starting from the overdamped Langevin dynamics in $\mathbb{R}^n$, $$ dX_t =
-\nabla V(X_t) dt + \sqrt{2 \beta^{-1}} dW_t, $$ we consider a scalar Markov
process $\xi_t$ which approximates the dynamics of the first component $X^1_t$.
In the previous work [F. Legoll, T. Lelievre, Nonlinearity 2010], the fact that
$(\xi_t)_{t \ge 0}$ is a good approximation of $(X^1_t)_{t \ge 0}$ is proven in
terms of time marginals, under assumptions quantifying the timescale separation
between the first component and the other components of $X_t$. Here, we prove
an upper bound on the trajectorial error $\mathbb{E} \left( \sup_{0 \leq t \leq
T} \left| X^1_t - \xi_t \right| \right)$, for any $T > 0$, under a similar set
of assumptions. We also show that the technique of proof can be used to obtain
quantitative averaging results.
