  Effective dynamics using conditional expectation was proposed in [F. Legoll
and T. Leli\`evre, Nonlinearity, 2010] to approximate the essential dynamics of
high-dimensional diffusion processes along a given reaction coordinate. The
approximation error of the effective dynamics when it is used to approximate
the behavior of the original dynamics has been considered in recent years. As a
continuation of the previous work [F. Legoll, T. Leli\`evre, and S. Olla,
Stoch. Process. Appl, 2017], in this paper we obtain pathwise estimates for
effective dynamics when the reaction coordinate function is either nonlinear or
vector-valued.
