Stopping and set-indexed local martingales

B. Gail Ivanoff and Ely Merzbach

Stochastic Processes and their Applications, 1995, vol. 57, issue 1, 83-98

Abstract: Set-indexed local martingales are defined and studied. We present some optional sampling theorems for strong martingales, martingales and weak martingales. The class of set-indexed processes which are locally of class (D) is introduced. A Doob-Meyer decomposition is obtained: any local weak submartingale has a unique decomposition into the sum of a local weak martingale and a local predictable increasing process. Finally some examples are given.

Keywords: Lattice; Set-indexed; martingale; Submartingale; Predictable; [sigma]-algebra; Stopping; set; Class; (D); Optional; sampling; Local; martingale; Doob-Meyer; decomposition (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (4)

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