×

zbMATH — the first resource for mathematics

L\({}^ p\) estimates on iterated stochastic integrals. (English) Zbl 0721.60052
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)

MSC:
60G44 Martingales with continuous parameter
60H05 Stochastic integrals
PDF BibTeX XML Cite
Full Text: DOI