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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A probabilistic approach to a boundary layer problem
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by Walter Vasilsky PDF
Trans. Amer. Math. Soc. 235 (1978), 375-385 Request permission

Abstract:

An elliptic second order linear operator is approximated by the transition operator of a Markov chain, and the solution to the corresponding approximate boundary value problem is expanded in terms of a small parameter, up to the first order term. In characterizing the boundary values of the first order term in the expansion, a problem of a boundary layer arises, which is treated by probabilistic methods.
References
  • P. R. Garabedian, Partial differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0162045
  • E. B. Dynkin, Infinitesimal operators of Markov processes, Teor. Veroyatnost. i Primenen. 1 (1956), 38–60 (Russian, with English summary). MR 0089540
  • W. Feller, An introduction to probability theory and its applications, Vol. 2, 2nd ed., Wjley, New York, 1971. MR 42 #5292.
  • George E. Forsythe and Wolfgang R. Wasow, Finite-difference methods for partial differential equations, Applied Mathematics Series, John Wiley & Sons, Inc., New York-London, 1960. MR 0130124
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 235 (1978), 375-385
  • MSC: Primary 60J60
  • DOI: https://doi.org/10.1090/S0002-9947-1978-0461686-1
  • MathSciNet review: 0461686