Filtrations for the two parameter jump process

Ata Al-Hussaini and Robert J. Elliott

Journal of Multivariate Analysis, 1985, vol. 16, issue 1, 118-139

Abstract: A process which has just one jump, and whose time parameter is the positive quadrant [0, [infinity]] - [0, [infinity]], is considered. Following Merzbach, related stopping lines are introduced, and the filtration {t1,t23} considered in this paper is such that, modulo completion, the [sigma]-field t1,t23 is the Borel field on the region Lt1,t2={(s1,s2); 0[less-than-or-equals, slant]s1[less-than-or-equals, slant]t1or0[less-than-or-equals, slant]s2[less-than-or-equals, slant]t2}, together with the atom which is the complement in [Omega] = [0, [infinity]]2 of Lt1,t2. Optional and predictable projections of related processes are defined, together with their dual projections, and an integral representation for martingales is obtained.

Keywords: Filtration; stopping; line; two; parameter; process; optional; projection; predictable; projection; martingale; representation (search for similar items in EconPapers)
Date: 1985
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