A stochastic differential equation is a differential equation containing one or more random driving stochastic processes. A scalar Itô equation is commonly written
 |
where 
is a Wiener process, 
is the drift coefficient,
and 
is the diffusion coefficient. Because sample paths
of a Wiener process are almost surely nowhere differentiable,
the equation is interpreted through stochastic
integrals rather than as an ordinary differential
equation along each path.
