  We define multiple stochastic integrals with respect to c\`{a}dl\`{a}g
martingales and prove moment bounds and chaos expansions, which allow to work
with them in a way similar to Wiener stochastic integrals. In combination with
the discretization framework of Erhard and Hairer (2017), our results give a
tool for proving convergence of interacting particle systems to stochastic PDEs
using regularity structures. As examples, we prove convergence of
martingale-driven discretizations of the $3$-dimensional stochastic
quantization equation and the KPZ equation.
