XIII: 50, 574-609, LNM 721 (1979)
JEULIN, Thierry
Grossissement d'une filtration et applications (
General theory of processes,
Markov processes)
This is a sequel to the papers
1209 and
1211, giving mostly applications of the theory of enlargements (turning a honest time $L$ into a stopping time) to Markov processes. The paper begins with a computation of conditional expectations relative to ${\cal F}_{L-}$, ${\cal F}_{L}$, ${\cal F}_{L+}$. This result is applied to coterminal times of a Markov process. Again a section is devoted to a general computation on two successive enlargements, which is shown to imply (with some work) Williams' well-known decomposition of Brownian paths
Keywords: Enlargement of filtrations,
Williams decompositionNature: Original
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XV: 15, 210-226, LNM 850 (1981)
JEULIN, Thierry;
YOR, Marc
Sur les distributions de certaines fonctionnelles du mouvement brownien (
Brownian motion)
This paper gives new proofs and extensions of results due to Knight, concerning occupation times by the process $(S_t,B_t)$ up to time $T_a$, where $(B_t)$ is Brownian motion, $T_a$ the hitting time of $a$, and $(S_t)$ is $\sup_{s\le t} B_s$. The method uses enlargement of filtrations, and martingales similar to those of
1306. Theorem 3.7 is a decomposition of Brownian paths akin to Williams' decomposition
Comment: See also
1516Keywords: Explicit laws,
Occupation times,
Enlargement of filtrations,
Williams decompositionNature: Original Retrieve article from Numdam
