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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
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