Abstract
A process which has just one jump, and whose time parameter is the positive quadrant [0, ∞] × [0, ∞], is considered. Following Merzbach, related stopping lines are introduced, and the filtration { F t 1, t 2 3} considered in this paper is such that, modulo completion, the σ-field F t 1, t 2 3 is the Borel field on the region L t1,t2={(s 1,s 2); 0⩽s 1⩽t 1 or0⩽s 2⩽t 2} , together with the atom which is the complement in Ω = [0, ∞] 2 of L t 1, t 2 . Optional and predictable projections of related processes are defined, together with their dual projections, and an integral representation for martingales is obtained.
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