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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 imbedding

Nature: Original

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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 processes

Nature: Original

Retrieve article from Numdam

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 $

Comment: A general survey on the Skorohod embedding problem is Ob\lój,

Keywords: Skorohod imbedding

Nature: Original

Retrieve article from Numdam

XVI: 17, 213-218, LNM 920 (1982)

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 processes

Nature: Original

Retrieve article from Numdam