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Matematicheskie Zametki, 2004, Volume 76, Issue 4, Pages 610–624
DOI: https://doi.org/10.4213/mzm124 (Mi mzm124) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Deviation Estimates for Random Walks and Stochastic Methods for Solving the Schrödinger Equation

A. M. Chebotarev, A. V. Polyakov

M. V. Lomonosov Moscow State University
Full-text PDF (359 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm124
Abstract: The stochastic representation of solutions of the Cauchy problem for the Schrödinger equation is used in order to construct unitary matrix approximations of the resolving operator. We show that the probability distribution of deviations of random walks allows one to estimate the increase rate of derivatives and the support of solutions.
Received: 12.05.2004
English version:
Mathematical Notes, 2004, Volume 76, Issue 4, Pages 564–577
DOI: https://doi.org/10.1023/B:MATN.0000043486.02521.da
Bibliographic databases:
UDC: 517.598
Language: Russian
Citation: A. M. Chebotarev, A. V. Polyakov, “Deviation Estimates for Random Walks and Stochastic Methods for Solving the Schrödinger Equation”, Mat. Zametki, 76:4 (2004), 610–624; Math. Notes, 76:4 (2004), 564–577
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm124
  • https://doi.org/10.4213/mzm124
  • https://www.mathnet.ru/eng/mzm/v76/i4/p610
    • This publication is cited in the following 2 articles:
    1. Faddeev M.M., Ibragimov I.A., Smorodina N.V., “a Stochastic Interpretation of the Cauchy Problem Solution For the Equation Partial Derivative(T)U = (SIGMA(2)/2)Delta U Plus V(X)U With Complex SIGMA”, Markov Process. Relat. Fields, 22:2 (2016), 203–226  mathscinet  zmath  isi
    2. Ibragimov I.A., Smorodina N.V., Faddeev M.M., “Limit Theorems For Symmetric Random Walks and Probabilistic Approximation of the Cauchy Problem Solution For Schrodinger Type Evolution Equations”, Stoch. Process. Their Appl., 125:12 (2015), 4455–4472  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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    Full-text PDF :258
    References:95
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