  In this paper we study from a numerical analysis perspective the Fractional
Step Kinetic Monte Carlo (FS-KMC) algorithms proposed in [1] for the parallel
simulation of spatially distributed particle systems on a lattice. FS-KMC are
fractional step algorithms with a time-stepping window $\Delta t$, and as such
they are inherently partially asynchronous since there is no processor
communication during the period $\Delta t$. In this contribution we primarily
focus on the error analysis of FS-KMC algorithms as approximations of
conventional, serial kinetic Monte Carlo (KMC). A key aspect of our analysis
relies on emphasising a goal-oriented approach for suitably defined macroscopic
observables (e.g., density, energy, correlations, surface roughness), rather
than focusing on strong topology estimates for individual trajectories.
  One of the key implications of our error analysis is that it allows us to
address systematically the processor communication of different parallelization
strategies for KMC by comparing their (partial) asynchrony, which in turn is
measured by their respective fractional time step $\Delta t$ for a prescribed
error tolerance.
