VI: 13, 151-158, LNM 258 (1972)
MEYER, Paul-André
Les résultats récents de Burkholder, Davis et Gundy (
Martingale theory)
The well-known norm equivalence between the maximum and the square-function of a martingale in moderate Orlicz spaces is presented following the celebrated papers of Burkholder-Gundy (
Acta Math., 124, 1970), Burkholder-Davis-Gundy (
Proc. 6-th Berkeley Symposium, 3, 1972). The technique of proof is now obsolete
Keywords: Burkholder inequalities,
Moderate convex functionsNature: Exposition
Retrieve article from Numdam
XII: 58, 770-774, LNM 649 (1978)
MEYER, Paul-André
Sur le lemme de La Vallée Poussin et un théorème de Bismut (
Measure theory,
General theory of processes)
Bismut proved that every optional process which belongs to the class (D) is the optional projection of a (non-adapted) process whose supremum is in $L^1$. This is given a more precise form, using the relation between uniform integrability and moderate Orlicz spaces
Keywords: Uniform integrability,
Class (D) processes,
Moderate convex functionsNature: Exposition,
Original additions Retrieve article from Numdam
XIV: 04, 26-48, LNM 784 (1980)
LENGLART, Érik;
LÉPINGLE, Dominique;
PRATELLI, Maurizio
Présentation unifiée de certaines inégalités de la théorie des martingales (
Martingale theory)
This paper is a synthesis of many years of work on martingale inequalities, and certainly one of the most influential among the papers which appeared in these volumes. It is shown how all main inequalities can be reduced to simple principles: 1) Basic distribution inequalities between pairs of random variables (``Doob'', ``domination'', ``good lambda'' and ``Garsia-Neveu''), and 2) Simple lemmas from the general theory of processes
Comment: This paper has been rewritten as Chapter XXIII of Dellacherie-Meyer,
Probabilités et Potentiel E ; see also
1621. A striking example of the power of these methods is Barlow-Yor, {\sl Jour. Funct. Anal.}
49,1982
Keywords: Moderate convex functions,
Inequalities,
Martingale inequalities,
Burkholder inequalities,
Good lambda inequalities,
Domination inequalitiesNature: Original Retrieve article from Numdam
XV: 20, 285-289, LNM 850 (1981)
CHOU, Ching Sung
Une inégalité de martingales avec poids (
Martingale theory)
Chevalier has strengthened the Burkholder inequalities into an equivalence of $L^p$ norms between $M^{\ast}\lor Q(M)$ and $M^{\ast}\land Q(M)$, where $M$ is a martingale, $M^{\ast}$ is its maximal function and $Q(M)$ its quadratic variation. This has been extended to all moderate Orlicz spaces in
1404. The present paper further extends the result to the Orlicz spaces of a law $\widehat P$ equivalent to $P$, provided the density is an $(A_p)$ weight (see
1326)
Keywords: Weighted norm inequalities,
Burkholder inequalities,
Moderate convex functionsNature: Original Retrieve article from Numdam
XVI: 11, 153-158, LNM 920 (1982)
MEYER, Paul-André
Interpolation entre espaces d'Orlicz (
Functional analysis)
This is an exposition of Calderon's complex interpolation method, in the case of moderate Orlicz spaces, aiming at its application in
1609Keywords: Interpolation,
Orlicz spaces,
Moderate convex functionsNature: Exposition Retrieve article from Numdam
