Journal of Theoretical Probability

, Volume 5, Issue 3, pp 585–596

Characterization ofO-summable processes

  • David Neal

DOI: 10.1007/BF01060438

Cite this article as:
Neal, D. J Theor Probab (1992) 5: 585. doi:10.1007/BF01060438


For a Banach-valued martingaleX, we define anL1-valued measureJX on an algebra of stochastic intervals which generates the optional σ-algebraO. We discuss conditions for when the measure has a countably additive extension toO, that is, for whenX isO-summable. For a process of integrable variationV, we define another countably additive measureIV onO. The existence of these measures allows for the definition of stochastic integrals of optional processes with respect to these Banach-valued processesX andV.

Key words

Stochastic integralvector-valued measuressummable andO-summable processes

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • David Neal
    • 1
  1. 1.Department of MathematicsWestern Kentucky UniversityBowling Green