Does any one know which book I can find the proof of martingale representation theorem in detail? I.E. Any $F_B$ adapted local martingale M is continuous and can be written as a integration of Brownian.
There is a proof on my notes. It says there exists a sequence of stopping times {$T_n$} such that $M^{T_n}$ is a bounded martingale. But we don't know M is continuous, I don't know how to construct a well-defined sequence of stopping times to make $M^{T_n}$ be a bounded martingale.
Thanks!