XIV: 12, 116-117, LNM 784 (1980)
CHOU, Ching Sung
Une caractérisation des semimartingales spéciales (
Stochastic calculus)
This is a useful addition to the next paper
1413: a semimartingale can be ``controlled'' (in the sense of Métivier-Pellaumail) by a locally integrable increasing process if and only if it is special
Comment: See also
1352Keywords: Semimartingales,
Métivier-Pellaumail inequality,
Special semimartingalesNature: Original
Retrieve article from Numdam
XIV: 13, 118-124, LNM 784 (1980)
ÉMERY, Michel
Équations différentielles stochastiques. La méthode de Métivier-Pellaumail (
Stochastic calculus)
Métivier-Pellaumail introduced the idea of an increasing process $(A_t)$ controlling a semimartingale $X$ as the property $$E[\,(sup_{t<T} \int_0^t H_s dX_s)^2\,] \le E[\,A_{T-}\,\int_0^{T-} H_s^2 dA_s\,]$$ for all stopping times $T$ and bounded previsible processes $(H_t)$. For a proof see
1414. Métivier-Pellaumail used this inequality to develop the theory of stochastic differential equations (including stability) without localization and pasting together at jump times. Here their method is applied to the topology of semimartingales
Comment: See
1352. A general reference on the Métivier-Pellaumail method can be found in their book
Stochastic Integration, Academic Press 1980. See also He-Wang-Yan,
Semimartingale Theory and Stochastic Calculus, CRC Press 1992
Keywords: Semimartingales,
Spaces of semimartingales,
Stochastic differential equations,
Doob's inequality,
Métivier-Pellaumail inequalityNature: Original Retrieve article from Numdam
XIV: 14, 125-127, LNM 784 (1980)
LENGLART, Érik
Sur l'inégalité de Métivier-Pellaumail (
Stochastic calculus)
A simplified (but still not so simple) proof of the Métivier-Pellaumail inequality
Keywords: Doob's inequality,
Métivier-Pellaumail inequalityNature: New proof of known results Retrieve article from Numdam
XIV: 24, 209-219, LNM 784 (1980)
PELLAUMAIL, Jean
Remarques sur l'intégrale stochastique (
Stochastic calculus)
This is an exposition of stochastic integrals and stochastic differential equations for Banach space valued processes along the lines of Métivier-Pellaumail
Stochastic Integration (1980), the class of semimartingales being defined by the Métivier-Pellaumail inequality (
1413)
Keywords: Stochastic integrals,
Stochastic differential equations,
Métivier-Pellaumail inequalityNature: Exposition Retrieve article from Numdam
XV: 33, 499-522, LNM 850 (1981)
STRICKER, Christophe
Quelques remarques sur la topologie des semimartingales. Applications aux intégrales stochastiques (
Stochastic calculus)
This paper contains a number of useful technical results on the topology of semimartingales (see
1324), some of which were previously known with more complicated proofs. In particular, it is shown how to improve the convergence of sequences of semimartingales by a convenient change of probability. The topology of semimartingales is used to handle elegantly the stochastic integration of previsible processes which are not locally bounded (see
1415). Finally, boundedness of a set of semimartingales is shown to be equivalent to the boundedness (in an elementary sense) of a set of increasing processes controlling them in the sense of Métivier-Pellaumail (see
1412,
1413,
1414)
Keywords: Semimartingales,
Stochastic integrals,
Spaces of semimartingales,
Métivier-Pellaumail inequalityNature: Original Retrieve article from Numdam
