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
312Keywords: Square integrable martingales,
Angle bracket,
Stochastic integralsNature: Exposition,
Original additions
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
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 integralsNature: Original Retrieve article from Numdam
