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L\({}^ 2\)-construction of distributions and the martingale problem. (Russian) Zbl 0706.60034

The article consists of two parts. The first one extends a general description of semimartingale distributions in Sobolev spaces \(H^ s_ 2\), \(s<1/2\), given in former author’s work [see the preceding review, Zbl 0706.60033], to those generated by pseudo-differential operators and contains predictable criteria of tightness, similar to the well-known ones of Jacod-Memin-Metivier in the Skorokhod topology. The second part is devoted to new existence and stability theorems on solutions of (semi- ) martingale problems.
Reviewer: E.I.Trofimov

MSC:

60F17 Functional limit theorems; invariance principles
60G17 Sample path properties
60H99 Stochastic analysis

Citations:

Zbl 0706.60033
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