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

Carlen, Eric; Krée, Paul

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)

MSC:

60G44	Martingales with continuous parameter
60H05	Stochastic integrals

Keywords:

Burkholder-Davis-Gundy type of inequality; iterated integrals; Neumann series for exponential martingales