Browse by: Author name - Classification - Keywords - Nature

11 matches found
II: 03, 34-42, LNM 51 (1968)
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 623
Nature: Original
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II: 04, 43-74, LNM 51 (1968)
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 equations
Nature: Exposition
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IV: 09, 77-107, LNM 124 (1970)
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 1017
Keywords: Local martingales, Stochastic integrals, Change of variable formula
Nature: Original
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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 law
Nature: Exposition
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V: 12, 127-137, LNM 191 (1971)
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, Supermartingales
Nature: Original
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V: 13, 138-140, LNM 191 (1971)
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 martingales
Nature: Original
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V: 14, 141-146, LNM 191 (1971)
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 integrals
Nature: Original
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XI: 24, 376-382, LNM 581 (1977)
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, Semimartingales
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XI: 25, 383-389, LNM 581 (1977)
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 inequalities
Nature: Original
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XIII: 16, 204-215, LNM 721 (1979)
Comment: An exponent $1/\lambda$ is missing in formula (4), p.315