In the study of non-stochastic differential equations usually one considers integrals of the
first kind, however for stochastic integral equations the right model is to generalise path
integrals. Lets consider how the path integral∫ baf (x) dx is defined. Let x0, x1, x2,..., xn∈ R
be points along a continuous path P from x0= a to xn= b. Note that we do not require that xi<
xi+ 1, so the path can both backtrack and leave the interval [a, b]. The path integral of f along
P is defined to be the limit of n− 1