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3 matches found
I: 06, 72-162, LNM 39 (1967)
MEYER, Paul-André
Intégrales stochastiques I--IV (4 talks) (Martingale theory, Stochastic calculus)
This series presents an expanded exposition of the celebrated paper of Kunita-Watanabe (Nagoya Math. J. 30, 1967) on square integrable martingales. The filtration is assumed to be free from fixed times of discontinuity, a restriction lifted in the modern theory. A new feature is the definition of the second increasing process associated with a square integrable martingale (a ``square bracket'' in the modern terminology). In the second talk, stochastic integrals are defined with respect to local martingales (introduced from Ito-Watanabe, Ann. Inst. Fourier, 15, 1965), and the general integration by parts formula is proved. Also a restricted class of semimartingales is defined and an ``Ito formula'' for change of variables is given, different from that of Kunita-Watanabe. The third talk contains the famous Kunita-Watanabe theorem giving the structure of martingale additive functionals of a Hunt process, and a new proof of Lévy's description of the structure of processes with independent increments (in the time homogeneous case). The fourth talk deals mostly with Lévy systems (Motoo-Watanabe, J. Math. Kyoto Univ., 4, 1965; Watanabe, Japanese J. Math., 36, 1964)
Comment: This paper was a step in the development of stochastic integration. Practically every detail of it has been reworked since, starting with Doléans-Dade-Meyer 409. Note a few corrections in Meyer 312
Keywords: Square integrable martingales, Angle bracket, Stochastic integrals
Nature: Exposition, Original additions
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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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X: 19, 414-421, LNM 511 (1976)
PRATELLI, Maurizio
Espaces fortement stables de martingales de carré intégrable (Martingale theory, Stochastic calculus)
This paper studies closed subspaces of the Hilbert space of square integrable martingales which are stable under optional stochastic integration (see 1018)
Keywords: Stable subpaces, Square integrable martingales, Stochastic integrals, Optional stochastic integrals
Nature: Original
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