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The Itô integral and near-martingales in Riesz spaces

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  • Mahin Sadat Divandar
  • Ghadir Sadeghi

Abstract

A new class of the Itô integral for Brownian motion is defined and studied in the framework of Riesz spaces. The stochastic process with respect to this stochastic integral is non-adapted and it is a motivitation to construct near-martingales in Riesz spaces. Furthermore, we state Doob–Meyer decomposition theorem for near-submartingales in Riesz spaces.

Suggested Citation

  • Mahin Sadat Divandar & Ghadir Sadeghi, 2023. "The Itô integral and near-martingales in Riesz spaces," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(14), pages 5068-5081, July.
    • Handle: RePEc:taf:lstaxx:v:52:y:2023:i:14:p:5068-5081
    DOI: 10.1080/03610926.2021.2003401
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