  The critical step in a molecular process is often a rare-event and has to be
simulated by an enhanced sampling protocol. Recovering accurate dynamical
estimates from such biased simulation is challenging. Girsanov reweighting is a
method to reweight dynamic properties formulated as path expected values. The
path probability is calculated at the time-step resolution of the
molecular-dynamics integrator. But the theory is largely limited to overdamped
Langevin dynamics. For underdamped Langevin dynamics, the absolute continuity
of the path probability ratio for the biased and unbiased potential is not
guaranteed, but it depends on the Langevin integrator. We develop a general
approach to derive the path probability ratio for Langevin integrators and to
analyze whether absolute continuity is fulfilled. We demonstrate our approach
on symmetric splitting methods for underdamped Langevin dynamics. For methods
that obey absolute continuity, and thus can be used for Girsanov reweighting,
we provide an expression for the relative path probability. %
