Doob-meyer decomposition for set-indexed submartingales

Marco Dozzi, B. Gail Ivanoff, Ely Merzbach

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10 Scopus citations


Set-indexed martingales and submartingales are defined and studied. The admissible function of a submartingale is defined and some class (D) conditions are given which allow the extension of the function to a σ-additive measure on the predictable σ-algebra. Then, we prove a Doob-Meyer decomposition: A set-indexed submartingale can be decomposed into the sum of a weak martingale and an increasing process. A hypothesis of predictability ensures the uniqueness of this decomposition. An explicit construction of the increasing process associated with a submartingale is given. Finally, some remarks, about quasimartingales are discussed.

Original languageEnglish
Pages (from-to)499-525
Number of pages27
JournalJournal of Theoretical Probability
Issue number3
StatePublished - Jul 1994
Externally publishedYes


  • Doob-Meyer decomposition
  • Lattice
  • admissible measure
  • class (D)
  • increasing process
  • predictable σ-algebra
  • quasimartingale
  • right-continuity
  • set-indexed martingale
  • stopping set
  • submartingale


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