A branch of mathematics that operates on stochastic processes.

Stochastic calculus allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. It is used to model systems that behave randomly.

The main flavours of stochastic calculus in Quantitative Finance are the Itô calculus and its variational relative the Malliavin calculus.

Source: https://en.wikipedia.org/wiki/Stochastic_calculus