Decomposition of Supermartingales Indexed by a Linearly Ordered Set
نویسنده
چکیده
We prove a version of the Doob Meyer decomposition for supermartingales with a linearly ordered index set. Key words Doob Meyer decomposition, natural increasing processes, potentials, supermartingales. Mathematics Subject Classi cation (2000): : 28A12, 60G07, 60G20.
منابع مشابه
Supermartingale Decomposition with a General Index Set
By Doob’s theorem, supermartingales indexed by the natural numbers decompose into the difference of a uniformly integrable martingale and an increasing process. The relative ease of working with increasing processes rather than supermartingales explains the prominent role of this result in stochastic analysis and in the theory of stochastic integration. Meyer [19] then proved that, under the us...
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