Email this article On a Limit Theorem Related to Probabilistic Representation of Solution to the Cauchy Problem for the Schrödinger Equation
- Authors: Ibragimov I.A.1, Smorodina N.V.1, Faddeev M.M.2
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Affiliations:
- St.Petersburg Department of the Steklov Mathematical Institute, St. Petersburg State University
- St. Petersburg State University
- Issue: Vol 229, No 6 (2018)
- Pages: 702-713
- Section: Article
- URL: https://journal-vniispk.ru/1072-3374/article/view/240523
- DOI: https://doi.org/10.1007/s10958-018-3709-0
- ID: 240523
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Abstract
A new method of probabilistic approximation of solution to the Cauchy problem for the unperturbed Schrödinger equation by expectations of functionals of a random walk is suggested. In contrast to earlier papers of the authors, the existence of exponential moment for each step of the random walk is not assumed.
About the authors
I. A. Ibragimov
St.Petersburg Department of the Steklov Mathematical Institute, St. Petersburg State University
Author for correspondence.
Email: ibr32@pdmi.ras.ru
Russian Federation, St. Petersburg
N. V. Smorodina
St.Petersburg Department of the Steklov Mathematical Institute, St. Petersburg State University
Email: ibr32@pdmi.ras.ru
Russian Federation, St. Petersburg
M. M. Faddeev
St. Petersburg State University
Email: ibr32@pdmi.ras.ru
Russian Federation, St. Petersburg
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