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The continuity of the quadratic variation of two-parameter martingales

It has been known that any L log+L-integrable two-parameter martingale M possesses a quadratic variation [M]. We show that the continuity properties of M are inherited by its quadratic variation. If M has no point jumps, [M] has no point jumps. [M] has at most axial jumps with respect to one of the coordinate axes in parameter space if M possesses this property. Finally, [M] is continuous along with M.
Year of publication:
1988
Authors: Frangos, Nikos E. ; Imkeller, Peter
Published in:
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 29.1988, 2, p. 267-279
Publisher: Elsevier
Keywords: two-parameter martingales quadratic variation point jumps axial jumps continuity
Type of publication: Article
Source:
Persistent link: https://www.econbiz.de/10008874032
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