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A note on the Doob-Meyer-decomposition of Lp-valued submartingales

Published online by Cambridge University Press:  17 April 2009

Bernhard Burgstaller
Bernhard Burgstaller
Affiliation:
Department of Financial Mathematics, Institute of Analysis, University of Linz, Altenberger Strasse 69, A-4040 Linz, Austria e-mail: [email protected]
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Let p > 1 real. We Doob-Meyer-decompose Lp(ℙ)-valued positive submartingales such that the martingale and predictable parts are also in Lp(ℙ). We give two variants of such a decomposition. The first one handles also not necessarily right continuous submartingales, since its proof is as discrete in its nature as Doob's archaically decomposition. The second decomposition acts in Lp (ℝ × Ω ℬ ⊗ ℱ, μ ⊗ ℙ) for some finite measure μ on ℝ.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 2 , April 2004 , pp. 227 - 235
Copyright
Copyright © Australian Mathematical Society 2004

References

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