Stochastic calculus is a calculus for processes driven by random noise, especially the Wiener process. Its central operation is the
stochastic integral 
, defined as a limit of sums whose integrands
are evaluated before the corresponding increments of 
.
An Itô process has the differential form 
. For a twice differentiable function
,
Itô's formula includes the quadratic-variation correction
 |
This correction distinguishes stochastic calculus from ordinary calculus and underlies stochastic differential equations and the Black-Scholes theory.
