Carlen, Eric; Krée, Paul L\({}^ p\) estimates on iterated stochastic integrals. (English) Zbl 0721.60052 Ann. Probab. 19, No. 1, 354-368 (1991). The authors prove a Burkholder-Davis-Gundy type of inequality for a sequence of iterated integrals relative to a bounded continuous martingale. The order of magnitude of the constants in the extreme members of the double inequality is given. This allows them, for example, to provide conditions for the \(L^ p\)-convergence of the Neumann series for exponential martingales; the a.s. convergence has earlier been established by C. Doleans-Dade. Reviewer: A.Gut (Uppsala) Cited in 3 ReviewsCited in 26 Documents MSC: 60G44 Martingales with continuous parameter 60H05 Stochastic integrals Keywords:Burkholder-Davis-Gundy type of inequality; iterated integrals; Neumann series for exponential martingales PDF BibTeX XML Cite \textit{E. Carlen} and \textit{P. Krée}, Ann. Probab. 19, No. 1, 354--368 (1991; Zbl 0721.60052) Full Text: DOI OpenURL