Chou, Ching-Sung Sur certaines généralisations de l’inégalité de Fefferman. (French) Zbl 0542.60047 Sémin. probabilités XVIII, 1982/83, Proc., Lect. Notes Math. 1059, 219-222 (1984). [For the entire collection see Zbl 0527.00020.] An extension of Fefferman’s inequality is given: suppose that X,Y are two semimartingales, the random variable \([Y,Y]_{\infty}\) is finite a.s., then \[ E\int^{\infty}_{0}| d[X,Y]_ s| \leq c E(\int^{\infty}_{0}Z^*_ sd[X,X]_ s)^{1/2} \] where \(Z^*_ t=\sup_{s\leq t}| Z_ s|\), Z is a unique optional positive process such that \(Z^ q_ T=E[([Y,Y]_{\infty}-[Y,Y]_{T-})^ q| F_ T]\) for any stopping time T and some \(q>0\). The constant c depends only on q. An extension of the inequality is given for an increasing moderate function and for a predictable case in which the process [\(\cdot,\cdot]\) is replaced by \(<\cdot,\cdot>\) when the last process exists. Reviewer: L.I.Gal’chuk Cited in 2 Documents MSC: 60G44 Martingales with continuous parameter 60H05 Stochastic integrals Keywords:Fefferman’s inequality; semimartingales Citations:Zbl 0527.00020 PDFBibTeX XML Full Text: Numdam EuDML