Asymptotics of integrals
نویسنده
چکیده
• Heuristic for Stirling’s asymptotic •Watson’s lemma •Watson’s lemma illustrated on B(s, a) • Simple form of Laplace’s method • Laplace’s method illustrated on Bessel functions Here some standard methods in asymptotic expansions [1] of integrals are illustrated: Watson’s lemma and Laplace’s method. Watson’s lemma dates from at latest [Watson 1918a], and Laplace’s method at latest from [Laplace 1774]. The exposition is revisionist: Laplace’s method is proven by reducing it to Watson’s lemma.
منابع مشابه
Asymptotic Approximation of Marginal Likelihood Integrals
We study the asymptotics of marginal likelihood integrals for discrete models using resolution of singularities from algebraic geometry, a method introduced recently by Sumio Watanabe. We briefly describe the statistical and mathematical foundations of this method, and explore how Newton diagrams and toric modifications help solve the problem. The approximations are then compared with exact com...
متن کاملIntegrals of Products of Hermite Functions
We compute the integrals of products of Hermite functions using the generating functions. The precise asymptotics of products of 4 Hermite functions are presented below. This estimate is relevant for the corresponding cubic nonlinear equation.
متن کاملAsymptotics and Mellin-Barnes Integrals
A catalogue record for this book is available from the British Library.
متن کاملRecursions and Asymptotics of Intersection Numbers
We establish the asymptotic expansion of certain integrals of ψ classes on moduli spaces of curves Mg,n when either the g or n goes to infinity. Our main tools are cut-join type recursion formulae from the WittenKontsevich theorem as well as asymptotics of solutions to the first Painlevé equation. We also raise a conjecture on large genus asymptotics for n-point functions of ψ classes and parti...
متن کاملTwo-point Taylor Expansions of Analytic Functions
In deriving uniform asymptotic expansions of a certain class of integrals one encounters the problem of expanding a function, that is analytic in some domain Ω of the complex plane, in two points. The first mention of the use of such expansions in asymptotics is given in [1], where Airy-type expansions are derived for integrals having two nearby (or coalescing) saddle points. This reference doe...
متن کاملAsymptotics for the infinite time ruin probability of a dependent risk model with a constant interest rate and dominatedly varying-tailed claim sizes
This paper mainly considers a nonstandard risk model with a constant interest rate, where both the claim sizes and the inter-arrival times follow some certain dependence structures. When the claim sizes are dominatedly varying-tailed, asymptotics for the infinite time ruin probability of the above dependent risk model have been given.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012