Laplace’s Method, Stationary Phase, Saddle Points, and a Theorem of Lalley

Stanley Sawyer
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Stanley Sawyer: Washington University, Department of Mathematics

A chapter in Harmonic Analysis and Discrete Potential Theory, 1992, pp 51-67 from Springer

Abstract: Abstract The purpose here is to discuss three useful asymptotic techniques from applied mathematics, and to illustrate them with a recent theorem of Steven Lalley. The techniques are (i) Laplace’s method, (ii) the method of stationary phase, and (iii) saddle point methods. The first item (Laplace’s method) is sufficiently elementary that you may have been using it for years without knowing that it had a name. The method of stationary phase is a complex analog, and saddle point methods are an amalgam of the two for contour integrals in the complex plane. See Erdélyi (1956) and Sirovich (1971) for more detail.

Keywords: Random Walk; Nonnegative Solution; Saddle Point Method; Martin Boundary; Smooth Real Function (search for similar items in EconPapers)
Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-2323-3_5

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DOI: 10.1007/978-1-4899-2323-3_5

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