Trofimov, E. I. L\({}^ 2\)-construction of distributions and the martingale problem. (Russian) Zbl 0706.60034 Izv. Vyssh. Uchebn. Zaved., Mat. 1990, No. 6(337), 67-77 (1990). 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 Cited in 1 Review MSC: 60F17 Functional limit theorems; invariance principles 60G17 Sample path properties 60H99 Stochastic analysis Keywords:Sobolev space; tightness; martingale problem; semimartingale distributions; Skorokhod topology Citations:Zbl 0706.60033 PDFBibTeX XMLCite \textit{E. I. Trofimov}, Izv. Vyssh. Uchebn. Zaved., Mat. 1990, No. 6(337), 67--77 (1990; Zbl 0706.60034)