Stochastic calculus is a branch of mathematics that operates on stochastic processes. The operations include integration and differentiation that involve both deterministic and random (i.e. stochastic) variables. It is used to model random behaviors encountered.
The most well-known stochastic process to which stochastic calculus is applied is the Wiener process (named in honor of Norbert Wiener), which is used for modelling Brownian motion as described by Albert Einstein and other physical diffusion processes in space of particles subject to random forces. More recently, the Wiener process has been widely applied in financial mathematics to model the evolution in time of stock and bond prices.
The main flavours of stochastic calculus are the Itô calculus and the Malliavin calculus.