Egbert Dettweiler
Embedding of general martingales into a Brownian motion
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 53, 75-110 (1999)
MSC:
60G44 Martingales with continuous parameter
square integrable random variable $X$ there is a Brownian motion
and a stopping time $\tau$ such that $X$ and $B_\tau$ have the
closeness of the distribution of $X$ to a normal distribution
$\nu_{0,s}$.