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Transactions of the American Mathematical Society

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



A probabilistic approach to a boundary layer problem

Author: Walter Vasilsky
Journal: Trans. Amer. Math. Soc. 235 (1978), 375-385
MSC: Primary 60J60
MathSciNet review: 0461686
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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 [Enhancements On Off] (What's this?)

  • 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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Article copyright: © Copyright 1978 American Mathematical Society