III: 15, 190-229, LNM 88 (1969)
MORANDO, Philippe
Mesures aléatoires (
Independent increments)
This paper consists of two talks, on the construction and structure of measures with independent values on an abstract measurable space, inspired by papers of Prekopa (
Acta Math. Acad. Sci. Hung., 7, 1956 and
8, 1957) and Kingman (
Pacific J. Math., 21, 1967)
Comment: If the measurable space is not ``too'' abstract, it can be imbedded into the line, and the standard theory of Lévy processes (non-homogeneous) can be used. This simple remark reduces the interest of the general treatment: see Dellacherie-Meyer,
Probabilités et potentiel, Chapter XIII, end of \S4
Keywords: Random measures,
Independent incrementsNature: Exposition,
Original additions
Retrieve article from Numdam
XI: 35, 502-517, LNM 581 (1977)
YOR, Marc
Remarques sur la représentation des martingales comme intégrales stochastiques (
Martingale theory)
The main result on the relation between the previsible representation property of a set of local martingales and the extremality of their joint law appeared in a celebrated paper of Jacod-Yor,
Z. für W-theorie, 38, 1977. Several concrete applications are given here, in particular a complete proof of a ``folklore'' result on the representation of local martingales of a Lévy process, and a discussion of the commutation problem of
1123Comment: This is an intermediate paper between the Jacod-Yor results and the definitive version of previsible representation, using the theorem of Douglas, for which see
1221Keywords: Previsible representation,
Extreme points,
Independent increments,
Lévy processesNature: Original Retrieve article from Numdam
XVI: 30, 348-354, LNM 920 (1982)
HE, Sheng-Wu;
WANG, Jia-Gang
The total continuity of natural filtrations (
General theory of processes)
Total continuity of a filtration ${\cal F}$ means that ${\cal F}_T={\cal F}_{T-}$ at every stopping time $T$, not necessarily previsible. It is shown that the filtration of a Lévy process without fixed discontinuities is totally continuous if and only if the jump size is a deterministic function of the jump time. Similarly, the natural filtration of a quasi-left continuous jump process is totally continuous if and only if the size of the $n$-th jump is a deterministic function of the jump times up to the $n$-th. It is shown that under the usual (here called ``strong'') previsible representation property, quasi-left continuity of the filtration implies total continuity
Keywords: Filtrations,
Independent increments,
Previsible representation,
Total continuity,
Lévy processesNature: Original Retrieve article from Numdam
XLV: 15, 365-400, LNM 2078 (2013)
PAGÈS, Gilles
Functional Co-monotony of Processes with Applications to Peacocks and Barrier Options (
Theory of processes)
Keywords: Co-monotony,
antithetic simulation method,
processes with independent increments,
Liouville processes,
fractional Brownian motion,
Asian options,
sensitivity,
barrier optionsNature: Original
