Burkholder, D. L. A sharp and strict \(L^ p\)-inequality for stochastic integrals. (English) Zbl 0617.60042 Ann. Probab. 15, 268-273 (1987). Let M be a right-continuous martingale, V be a predictable process, \(N=V\circ M\) (stochastic integral of V with respect to M). Let \(p^*\) be the maximum of p and q where \(1<p<\infty\) and \(1/p+1/q=1\). Set \(\| M\|_ p=\sup_{t}\| M_ t\|_ p.\) Theorem. If \(p=2\) and \(0<\| M\|_ p<\infty\), then \[ \| N\|_ p<(p^*-1)\| M\|_ p \] [strict inequality in contrast with a previous result of the author, see ibid. 12, 647-702 (1984; Zbl 0556.60021)]. Reviewer: Yu.M.Kabanov Cited in 18 Documents MSC: 60G44 Martingales with continuous parameter 26D15 Inequalities for sums, series and integrals 60H05 Stochastic integrals Keywords:norm inequalities; right-continuous martingale; predictable process Citations:Zbl 0556.60021 PDFBibTeX XMLCite \textit{D. L. Burkholder}, Ann. Probab. 15, 268--273 (1987; Zbl 0617.60042) Full Text: DOI