Does it make sense to define the Stratonovich integral like this ? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T08:26:50Z http://mathoverflow.net/feeds/question/38501 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/38501/does-it-make-sense-to-define-the-stratonovich-integral-like-this Does it make sense to define the Stratonovich integral like this ? Kevin 2010-09-12T18:51:01Z 2010-09-12T19:41:33Z <p>Does it make sense to define the Stratonovich integral like this ? $I_{s}(t)=\int^{t}_{s}F(f_s(u),\circ du):= \lim_{\Delta \to 0} in\ pr. \Sigma^{n-1}_{k=0}\frac{1}{2} \Big( F(f_s(t_{k+1}),t_{k+1})$ $+F(f_s(t_{k}),t_{k+1})-F(f_s(t_{k+1}),t_{k}) -F(f_s(t_{k}),t_{k}) \Big)$ where $F(x,t,\omega)$ is a semimartingale helix and $f_s (t)$ is a semimartingale and $\Delta :=\max(t_{k+1}-t_k)$. The common version is $\Sigma \big( X_{t_{k+1}}+X_{t_{k}} \big)/2 \big( W_{t_{k+1}}-W_{t_{k}} \big).$ How do they become equivalent to each other?</p>