Lq‐valued Burkholder–Rosenthal inequalities and sharp estimates for stochastic integrals

Lq‐valued Burkholder–Rosenthal inequalities and sharp estimates for stochastic integrals

We prove sharp maximal inequalities for Lq‐valued stochastic integrals with respect to any Hilbert space‐valued local martingale. Our proof relies on new Burkholder–Rosenthal type inequalities for martingales taking values in an Lq‐space.

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Bibliographische Detailangaben
Veröffentlicht in:Proceedings of the London Mathematical Society 2019-12, Vol.119 (6), p.1633-1693
Hauptverfasser: Dirksen, Sjoerd, Yaroslavtsev, Ivan
Format: Artikel
Sprache:eng
Schlagworte:
46L52 (secondary)
60G42
60G44
60H05 (primary)
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Beschreibung
Zusammenfassung:We prove sharp maximal inequalities for Lq‐valued stochastic integrals with respect to any Hilbert space‐valued local martingale. Our proof relies on new Burkholder–Rosenthal type inequalities for martingales taking values in an Lq‐space.
ISSN:0024-6115
1460-244X
DOI:10.1112/plms.12277