  In this paper we study the deterministic and stochastic homogenisation of
free-discontinuity functionals under \emph{linear} growth and coercivity
conditions. The main novelty of our deterministic result is that we work under
very general assumptions on the integrands which, in particular, are not
required to be periodic in the space variable. Combining this result with the
pointwise Subadditive Ergodic Theorem by Akcoglu and Krengel, we prove a
stochastic homogenisation result, in the case of stationary random integrands.
In particular, we characterise the limit integrands in terms of asymptotic cell
formulas, as in the classical case of periodic homogenisation.
