Parabolic Itô equations
Parabolic Itô equations
A parabolic Itô equation is an equation of the form \[ (\partial u/\partial t)(t,\omega ) = Lu(t,\omega ) + f(u(t,\omega )) + \alpha (t,\omega ),\quad u(0) = {u_0},{u_0},u \in H.\] $H$ is a Hilbert space with scalar product $u \cdot \upsilon$ and norm $| \cdot |$. $L$ is a linear …