  We develop a study of ignorability and conditions thereof for likelihood
inference in the framework of stochastic processes. We define a coarsening
model for processes which includes discrete-time observations as well as
censored continuous-time observations and applies to continuous state-space
processes as well as counting processes. For preparing the work we recall
formulas for manipulating marginal and conditional likelihood ratios (which can
apply to stochastic processes). Ignorability is defined in terms of local
equality of two likelihood ratios. We give static conditions of ignorability
and then dynamical conditions which are more interpretable. We illustrate the
use of the dynamical conditions of ignorability in problems of censoring,
missing data and joint modelling.
