Editing Stochastic differential equation (section)

===Stochastic calculus===
[[Brownian motion]] or the [[Wiener process]] was discovered to be exceptionally complex mathematically. The [[Wiener process]] is almost surely nowhere differentiable;<ref name="rogerswilliams"/><ref name="oksendal"/> thus, it requires its own rules of calculus. There are two dominating versions of stochastic calculus, the [[Itô calculus|Itô stochastic calculus]] and the [[Stratonovich stochastic calculus]]. Each of the two has advantages and disadvantages, and newcomers are often confused whether the one is more appropriate than the other in a given situation. Guidelines exist (e.g. Øksendal, 2003)<ref name="oksendal">{{cite book
| last = Øksendal
| first = Bernt K.
| author-link = Bernt Øksendal
| title=Stochastic Differential Equations: An Introduction with Applications
| publisher=Springer
| location = Berlin
| year=2003
| isbn=3-540-04758-1
}}</ref> and conveniently, one can readily convert an Itô SDE to an equivalent Stratonovich SDE and back again.<ref name="rogerswilliams"/><ref name="oksendal"/> Still, one must be careful which calculus to use when the SDE is initially written down.