  The recent study by B. De Bruyne, S. N. Majumdar, H. Orland and G. Schehr
[arXiv:2110.07573], concerning the conditioning of the Brownian motion and of
random walks on global dynamical constraints over a finite time-window $T$, is
reformulated as a general framework for the 'microcanonical conditioning' of
Markov processes on time-additive observables. This formalism is applied to
various types of Markov processes, namely discrete-time Markov chains,
continuous-time Markov jump processes and diffusion processes in arbitrary
dimension. In each setting, the time-additive observable is also fully general,
i.e. it can involve both the time spent in each configuration and the
elementary increments of the Markov process. The various cases are illustrated
via simple explicit examples. Finally, we describe the link with the 'canonical
conditioning' based on the generating function of the time-additive observable
for finite time $T$, while the regime of large time $T$ allows to recover the
standard large deviation analysis of time-additive observables via the deformed
Markov operator approach.
