Regularity and decomposition of two-parameter supermartingales

G. Mazziotto, E. Merzbach

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The well-known Doob-Meyer decomposition of a supermartingale as the difference of a martingale and an increasing process is extended in several ways for two-parameter stochastic processes. In particular, the notion of laplacian is introduced which gives more explicit decomposition for potentials. The optional sampling theorem is stated for a wide class of supermartingales justifying the study of local martingales. Conditions for regularity and continuity for two-parameter processes are given using approximate laplacians. By introducing the notion of optional increasing path, the relation between the regularity of certain quasimartingales and the continuity of the associated integrable variation process is proved.

Original languageEnglish
Pages (from-to)38-55
Number of pages18
JournalJournal of Multivariate Analysis
Issue number1
StatePublished - Aug 1985


  • Stopping points
  • optional increasing paths
  • potential
  • regularity
  • supermartingales
  • two-parameter processes


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