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Teoriya Veroyatnostei i ee Primeneniya, 2019, Volume 64, Issue 1, Pages 3–16
DOI: https://doi.org/10.4213/tvp5230 (Mi tvp5230) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On the completeness of stochastic flows generated by equations with current velocities

Yu. E. Gliklikh, T. A. Shchichko

Voronezh State University
Full-text PDF (485 kB) Citations (4)
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DOI: https://doi.org/10.4213/tvp5230
Abstract: Sufficient conditions as well as necessary and sufficient ones are found for the completeness of the stochastic flow generated by equations with the so-called current velocities (Nelson's symmetric mean derivatives). A characteristic property of such equations is that the solvability of the Cauchy problem (the existence of orbits of the flow) is proved only under the assumption that the initial value is a random variable such that its distribution density is smooth and nowhere vanishes.
Keywords: mean derivatives, current velocities, stochastic flows, completeness, continuity at infinity.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00048
This work was supported by the Russian Foundation for Basic Research (grant 18-01-00048).
Received: 18.06.2018
Revised: 06.09.2018
Accepted: 18.10.2018
English version:
Theory of Probability and its Applications, 2019, Volume 64, Issue 1, Pages 1–11
DOI: https://doi.org/10.1137/S0040585X97T989350
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Yu. E. Gliklikh, T. A. Shchichko, “On the completeness of stochastic flows generated by equations with current velocities”, Teor. Veroyatnost. i Primenen., 64:1 (2019), 3–16; Theory Probab. Appl., 64:1 (2019), 1–11
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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