Different kinds of two-parameter martingales

Ely Merzbach, David Nualart

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This paper is devoted to the study of all the different classes of two-parameter martingales which were introduced during the last decade. The problem of the relations between these classes is completely solved under the F-4 assumption and counter-examples are given in order to point out the differences between these classes. Characterizations in terms of Doob-Meyer-Cairoli decompositions are obtained. In the case where the filtration is generated by a two-parameter Poisson process, we prove that the class of strong martingales coincides with the class of martingales of direction independent variation.

Original languageEnglish
Pages (from-to)193-208
Number of pages16
JournalIsrael Journal of Mathematics
Issue number3
StatePublished - Dec 1985


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