XIV: 40, 357-391, LNM 784 (1980)
FALKNER, Neil
On Skorohod embedding in $n$-dimensional Brownian motion by means of natural stopping times (
Brownian motion,
Potential theory)
The problem discussed here is the Skorohod representation of a measure $\nu$ as the distribution of $B_T$, where $(B_t)$ is Brownian motion in $
R^n$ with the initial measure $\mu$, and $T$ is a
non-randomized stopping time. The conditions given are sufficient in all cases, necessary if $\mu$ does not charge polar sets
Comment: A general survey on the Skorohod embedding problem is Ob\lój,
Probab. Surv. 1, 2004
Keywords: Skorohod imbeddingNature: Original
Retrieve article from Numdam
XVI: 17, 213-218, LNM 920 (1982)
FALKNER, Neil;
STRICKER, Christophe;
YOR, Marc
Temps d'arrêt riches et applications (
General theory of processes)
This paper starts from the existence of increasing left-continuous processes $(A_t)$ which generate the previsible $\sigma$-field, i.e., every previsible process can be represented as $f(X_t)$ for some Borel function $f$ (see
1123), to prove the existence (discovered by the first named author) of ``rich'' stopping times $T$, i.e., previsible stopping times which encode the whole past up to time $T$: $\sigma(T)={\cal F}_{T-}$ (a few details are omitted here). This result leads to counterexamples: a non-reversible semimartingale (see the preceding paper
1616) and a stopping time $T$ for Brownian motion such that $L^a_T$ is not a semimartingale in its space variable $a$
Keywords: Stopping times,
Local times,
Semimartingales,
Previsible processesNature: Original Retrieve article from Numdam
