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Normed supports and limit theorems for semimartingales. (Russian) Zbl 0714.60040

As theory of Sobolev-like spaces is being an important tool of analysis and applications, it is of interest to embed a random process into such spaces. The author shows that almost all paths of any semimartingale (X(t); \(t\geq 0)\) belong to the Besov-Nikolski spaces \(B^ s_{pq}({\mathbb{R}}_+)_{loc}\) for any \(1\leq p<\infty\), \(1\leq q\leq \infty\) and appropriate \(s>0\). Thus the paths are smooth, in this sense, and X gives rise to a Borelian element in such a space. New tightness criteria and a functional limit theorem on convergence to a process with conditionally independent increments are obtained. It is to be noticed, that Theorem 5 of the work needs some additional conditions to be true and shall be given in a correct formulation elsewhere.
Reviewer: E.I.Trofimov

MSC:

60G60 Random fields
62H99 Multivariate analysis
62F99 Parametric inference
62K99 Design of statistical experiments
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