Strong Martingales: Their Decompositions and Quadratic Variation

Dean Slonowsky ()
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Dean Slonowsky: University of Manitoba

Journal of Theoretical Probability, 2001, vol. 14, issue 3, 609-638

Abstract: Abstract Set-indexed strong martingales and a form of predictability for set-indexed processes are defined. Under a natural integrability condition, we show that any set-indexed strong submartingale can be decomposed in the Doob–Meyer sense. A form of predictable quadratic variation for square-integrable set-indexed strong martingales is defined and sufficient conditions for its existence are given. Under a conditional independence assumption, these reduce to a simple moment condition and, if the strong martingale has continuous sample paths, the resulting quadratic variation can be approximated in the L 2-sense by sums of conditional expectations of squared increments.

Keywords: set-indexed strong submartingale; increasing process; predictability; Doob–Meyer decomposition; quadratic variation; discrete approximations (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1017536921656

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