確率解析

伊藤積分

$ \int_b^a\Phi(x(t),t)dx(t)=\lim_{\varDelta\to 0}\sum_{j=1}^{N-1}\Phi(x(t_j),t_j)(x(t_{j+1})-x(t_j))

$ \varDelta=\max(t_{j+1}-t_j)

Стратоновича 積分

$ \int_b^a\Phi(x(t),t)\circ dx(t)=\lim_{\varDelta\to 0}\sum_{j=1}^{N-1}\Phi\left(\frac{x(t_j)+x(t_{j+1})}2,t_j\right)(x(t_{j+1})-x(t_j))

$ \varDelta=\max(t_{j+1}-t_j)