  Given a general It\^o semimartingale, its Markovian projection is an It\^o
process, with Markovian differential characteristics, that matches the
one-dimensional marginal laws of the original process. We construct Markovian
projections for It\^o semimartingales with jumps, whose flows of
one-dimensional marginal laws are solutions to non-local
Fokker--Planck--Kolmogorov equations (FPKEs). As an application, we show how
Markovian projections appear in building calibrated diffusion/jump models with
both local and stochastic features.
