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

60J65 Brownian motion, See also {58G32}

Abstract: In 1960 Skorohod proved [10] that for any mean zero,
square integrable random variable $X$ there is a Brownian motion
and a stopping time $\tau$ such that $X$ and $B_\tau$ have the
same distribution. Meanwhile there exist a series of different,
elegant proofs of this so-called Skorohod embedding (cf. [1], [2], [4], [11] and
[5]). This embedding gives the possibility to measure the
closeness of the distribution of $X$ to a normal distribution
$\nu_{0,s}$.
Keywords: Martingales with continuous parameter, Brownian motion, Diffusion processes and stochastic analysis on manifolds