II: 03, 34-42, LNM 51 (1968)
DOLÉANS-DADE, Catherine
Fonctionnelles additives parfaites (
Markov processes)
The identity defining additive (or multiplicative) functionals involves an exceptional set depending on a continuous time $t$. If the exceptional set can be chosen independently of $t$, the functional is perfect. It is shown that every additive functional of a Hunt process admitting a reference measure has a perfect version
Comment: The existence of a reference measure was lifted by Dellacherie in
304. However, the whole subject of perfect additive functionals has been closed by Walsh's approach using the essential topology, see
623Keywords: Additive functionals,
PerfectionNature: Original
Retrieve article from Numdam
II: 04, 43-74, LNM 51 (1968)
DOLÉANS-DADE, Catherine
Espaces $H^m$ sur les variétés, et applications aux équations aux dérivées partielles sur une variété compacte (
Functional analysis)
An attempt to teach to the members of the seminar the basic facts of the analytic theory of diffusion processes
Keywords: Sobolev spaces,
Second order elliptic equationsNature: Exposition Retrieve article from Numdam
IV: 09, 77-107, LNM 124 (1970)
DOLÉANS-DADE, Catherine;
MEYER, Paul-André
Intégrales stochastiques par rapport aux martingales locales (
Martingale theory,
Stochastic calculus)
This is a continuation of Meyer
106, with a new complete exposition of the theory, and two substantial improvements: the filtration is general (while in
106 it was assumed free of fixed times of discontinuity) and the definition of semimartingales is the modern one (while in
106 they were the special semimartingales of nowadays). The change of variables formula is given in its full generality
Comment: The results of this paper have become classical, and are reproduced almost literally in Meyer
1017Keywords: Local martingales,
Stochastic integrals,
Change of variable formulaNature: Original Retrieve article from Numdam
IV: 19, 240-282, LNM 124 (1970)
DELLACHERIE, Claude;
DOLÉANS-DADE, Catherine;
LETTA, Giorgio;
MEYER, Paul-André
Diffusions à coefficients continus, d'après Stroock et Varadhan (
Markov processes,
Diffusion theory)
This paper consists of four seminar talks on a celebrated paper of Stroock-Varadhan (
Comm. Pure Appl. Math.,
22, 1969), which constructs by a probability method a unique semigroup whose generator is an elliptic second order operator with continuous coefficients (the analytic approach either deals with operators in divergence form, or requires some Hölder condition). The contribution of G.~Letta nicely simplified the proof
Comment: The results were so definitive that apparently the subject attracted no further work. See Stroock-Varadhan,
Multidimensional Diffusion Processes, Springer 1979
Keywords: Elliptic differential operators,
Uniqueness in lawNature: Exposition Retrieve article from Numdam
V: 12, 127-137, LNM 191 (1971)
DELLACHERIE, Claude;
DOLÉANS-DADE, Catherine
Un contre-exemple au problème des laplaciens approchés (
Martingale theory)
The ``approximate Laplacian'' method of computing the increasing process associated with a supermartingale does not always converge in the strong sense: solves a problem open for many years
Comment: Problem originated in Meyer,
Ill. J. Math.,
7, 1963
Keywords: Submartingales,
SupermartingalesNature: Original Retrieve article from Numdam
V: 13, 138-140, LNM 191 (1971)
DOLÉANS-DADE, Catherine
Une martingale uniformément intégrable, non localement de carré intégrable (
Martingale theory)
Now well known! This paper helped to set the basic notions of the theory
Keywords: Square integrable martingalesNature: Original Retrieve article from Numdam
V: 14, 141-146, LNM 191 (1971)
DOLÉANS-DADE, Catherine
Intégrales stochastiques par rapport à une famille de probabilités (
Stochastic calculus)
Given a family of probability laws on the same space, construct versions of stochastic integrals which do not depend on the law
Comment: Expanded by Stricker-Yor, Calcul stochastique dépendant d'un paramètre,
Z. für W-theorie, 45, 1978
Keywords: Stochastic integralsNature: Original Retrieve article from Numdam
XI: 24, 376-382, LNM 581 (1977)
DOLÉANS-DADE, Catherine;
MEYER, Paul-André
Équations différentielles stochastiques (
Stochastic calculus)
This is an improved and simplified exposition of the existence and uniqueness theorem for solutions of stochastic differential equations with respect to semimartingales, as proved by the first author in
Zeit. für W-theorie, 36, 1976 and by Protter in
Ann. Prob. 5, 1977. The theory has become now so classical that the paper has only historical interest
Keywords: Stochastic differential equations,
SemimartingalesNature: Exposition,
Original additions Retrieve article from Numdam
XI: 25, 383-389, LNM 581 (1977)
DOLÉANS-DADE, Catherine;
MEYER, Paul-André
Une caractérisation de $BMO$ (
Martingale theory)
Kazamaki gave in
1027 a criterion for a continuous martingale to belong to $BMO$, involving its stochastic exponential. This criterion is extended, though in a different form, to non-continuous local martingales: $M$ belongs to $BMO$ if and only if for $|\lambda|$ small enough, its stochastic exponential ${\cal E}(\lambda M)$ is a (positive) multiplicatively bounded process---a class of processes, which looked promising but did not attract attention
Comment: Related subjects occur in
1328. The reference to ``note VI'' on p.384 probably refers to an earlier preprint, and is no longer intelligible
Keywords: $BMO$,
Stochastic exponentials,
Martingale inequalitiesNature: Original Retrieve article from Numdam
XIII: 16, 204-215, LNM 721 (1979)
DOLÉANS-DADE, Catherine;
MEYER, Paul-André
Un petit théorème de projection pour processus à deux indices (
Several parameter processes)
This paper proves a previsible projection theorem in the case of two-parameter processes, with a two-parameter filtration satisfying the standard commutation property of Cairoli-Walsh. The idea is to apply successively the projection operation of
1315 to the two coordinates
Keywords: Previsible processes (several parameters),
Previsible projections,
Random measuresNature: Original Retrieve article from Numdam
XIII: 28, 313-331, LNM 721 (1979)
DOLÉANS-DADE, Catherine;
MEYER, Paul-André
Inégalités de normes avec poids (
Martingale theory)
See the review of
1326. This is a rather systematic exposition of the subject in the frame of martingale theory
Comment: An exponent $1/\lambda$ is missing in formula (4), p.315
Keywords: Weighted norm inequalitiesNature: Exposition,
Original additions Retrieve article from Numdam
