Stochastic calculus - Definition and Overview

Stochastic calculus is a branch of mathematics that provides the formal framework and mathematical tools needed for modelling stochastic processes, which are specified through one or more integral and/or differential equations involving both deterministic and random (i.e. stochastic) variables.

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 Ito calculus and the Malliavin calculus.

Example Usage of Stochastic