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Avtomatika i Telemekhanika, 2020, Issue 3, Pages 28–43
DOI: https://doi.org/10.31857/S0005231020030034 (Mi at15435) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Topical issue

On weak solutions of highly degenerate SDEs

A. Yu. Veretennikovabc

a University of Leeds, Leeds, United Kingdom
b National Research University Higher School of Economics, Moscow, Russia
c Kharkevich Institute for Information Transmission Problems, Moscow, Russia
Full-text PDF (329 kB) Citations (4)
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DOI: https://doi.org/10.31857/S0005231020030034
Abstract: The existence and weak uniqueness of a weak solution of a highly degenerate stochastic differential equation, along with its local mixing property, are established via Girsanov's transformation.
Keywords: stochastic differential equation, weak solution, weak uniqueness, local mixing, Girsanov transformation.
Funding agency Grant number
HSE Basic Research Program
Ministry of Education and Science of the Russian Federation
Russian Science Foundation 17-11-01098
This work was supported by the Russian Academic Excellence Project “5-100”; the part related to Theorem 3 was supported by the Russian Science Foundation, project no. 17-11-01098.
Presented by the member of Editorial Board: B. M. Miller

Received: 20.06.2019
Revised: 14.08.2019
Accepted: 26.09.2019
English version:
Automation and Remote Control, 2020, Volume 81, Issue 3, Pages 398–410
DOI: https://doi.org/10.1134/S0005117920030029
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. Yu. Veretennikov, “On weak solutions of highly degenerate SDEs”, Avtomat. i Telemekh., 2020, no. 3, 28–43; Autom. Remote Control, 81:3 (2020), 398–410
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/at15435
  • https://www.mathnet.ru/eng/at/y2020/i3/p28
    • This publication is cited in the following 4 articles:
    1. Yaozhong Hu, Michael A. Kouritzin, Jiayu Zheng, “Nonlinear McKean-Vlasov Diffusions under the Weak Hörmander Condition with Quantile-Dependent Coefficients”, Potential Anal, 60:3 (2024), 1093  crossref
    2. Alexander Veretennikov, “On weak existence of solutions of degenerate McKean–Vlasov equations”, Stoch. Dyn., 24:05 (2024)  crossref
    3. Paolo Pigato, “Density estimates and short-time asymptotics for a hypoelliptic diffusion process”, Stochastic Processes and their Applications, 145 (2022), 117  crossref
    4. A. Veretennikov, “Note on local mixing techniques for stochastic differential equations”, Mod. Stoch.-Theory Appl., 8:1 (2021), 1–15  crossref  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Avtomatika i Telemekhanika
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    Abstract page:234
    Full-text PDF :55
    References:39
    First page:24
     
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