Editing Stochastic calculus (section)

== Stratonovich integral ==
{{main|Stratonovich integral}}

The Stratonovich integral or Fisk–Stratonovich integral of a [[semimartingale]] <math>X</math> against another [[semimartingale]] ''Y'' can be defined in terms of the Itô integral as

:<math>\int_0^t X_{s-} \circ d Y_s : = \int_0^t X_{s-} d Y_s + \frac{1}{2} \left [ X, Y\right]_t^c,</math>

where [''X'',&nbsp;''Y'']<sub>''t''</sub><sup>''c''</sup> denotes the optional [[Quadratic variation|quadratic covariation]] of the continuous parts of ''X''
and&nbsp;''Y'', which is the optional quadratic covariation minus the jumps of the processes <math>X</math> and <math>Y</math>, i.e.
:<math>\left [ X, Y\right]_t^c:=
[X,Y]_t - \sum\limits_{s\leq t}\Delta X_s\Delta Y_s</math>.
The alternative notation

:<math>\int_0^t X_s \, \partial Y_s</math>

is also used to denote the Stratonovich integral.