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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 increments

Nature: Exposition, Original additions

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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 1123

Comment: 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 1221

Keywords: Previsible representation, Extreme points, Independent increments, Lévy processes

Nature: Original

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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 processes

Nature: Original

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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 options

Nature: Original

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 (

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,

Keywords: Random measures, Independent increments

Nature: Exposition, Original additions

Retrieve article from Numdam

XI: 35, 502-517, LNM 581 (1977)

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,

Comment: 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 1221

Keywords: Previsible representation, Extreme points, Independent increments, Lévy processes

Nature: Original

Retrieve article from Numdam

XVI: 30, 348-354, LNM 920 (1982)

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 processes

Nature: Original

Retrieve article from Numdam

XLV: 15, 365-400, LNM 2078 (2013)

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 options

Nature: Original