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A Distributional Theory of Asymptotic Expansions
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1990Abstract We present various techniques for the asymptotic expansions of generalized functions. We show that the moment asymptotic expansions hold for a very wide variety of kernels such as generalized functions of rapid decay and rapid oscillations.
R Estrada, R. P Kanwal
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Applicable Algebra in Engineering, Communication and Computing, 1998
The author gives an expansion algorithm for germs of exp-log functions at infinity, which is correct modulo Schanuel's conjecture. He also shows how the algorithm can be made generic.
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The author gives an expansion algorithm for germs of exp-log functions at infinity, which is correct modulo Schanuel's conjecture. He also shows how the algorithm can be made generic.
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Asymptotic expansions by Γ-convergence
Continuum Mechanics and Thermodynamics, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Braides A., Truskinovsky L.
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On Multiple Asymptotic Expansions
SIAM Journal on Mathematical Analysis, 1972In previous papers asymptotic meaning has been attached to the formal double sums $\sum _{m = 0}^\infty \sum _{n = 0}^\infty a_{mn} x^{ - n} e^{ - \lambda mx} (\lambda > 0)$ as $x \to 0$ in a sector of the right half-plane. Formal applications of these sums to elastic scattering and to singular perturbation problems have also been given.
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Asymptotic expansions at work.
Insurance: Mathematics and Economics, 1995Abstract 1. NORMAL APPROXIMATIONS It is routine among applied statisticians to use normal approximations. One of the most classical results being for the maximum likelihood estimate θ^ based on n i.i.d. observations from a density with expected information i(θ).
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Journal of the London Mathematical Society, 1949
Die Differentialgleichung der Bessel-Funktionen wird durch die Transformation \(w = \sqrt{\zeta} J_\nu(\lambda\sqrt{1-\zeta^2})\), \(u = \mathfrak{ArTg}\,\zeta - \zeta\) in die Form gebracht: \[ d^2w/du^2 + w\{- \nu^2 + (\zeta^{-2} - 1) [\tfrac54 \zeta^{-4}+ \tfrac14 \zeta^{-2} + \lambda^2 - \nu^2)]\} = 0, \tag{1} \] wo \(\lambda\) eine geeignet ...
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Die Differentialgleichung der Bessel-Funktionen wird durch die Transformation \(w = \sqrt{\zeta} J_\nu(\lambda\sqrt{1-\zeta^2})\), \(u = \mathfrak{ArTg}\,\zeta - \zeta\) in die Form gebracht: \[ d^2w/du^2 + w\{- \nu^2 + (\zeta^{-2} - 1) [\tfrac54 \zeta^{-4}+ \tfrac14 \zeta^{-2} + \lambda^2 - \nu^2)]\} = 0, \tag{1} \] wo \(\lambda\) eine geeignet ...
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Perturbation Expansion: Is it Asymptotic?
Modern Physics Letters A, 1997It is pointed out that, for any model with bound state, contrary to the case of nonrelativistic quantum mechanics, perturbation expansion based on Feynman rules in relativistic quantum field theory is not asymptotic of physical amplitude in which the effects of bound state are considered.
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On Multivariable Asymptotic Expansions
SIAM Review, 1971In this paper we consider the damped linear oscillator with small damping $\varepsilon $. We obtain uniform asymptotic expansions of the solution as $\varepsilon \to 0$ that are uniformly valid for all time $t \geqq 0$, by the multitime method. We show how to determine the expansion coefficients without resorting to intuitive arguments. This is done by
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Asymptotic expansion for splines
1983The author extends some of the previous results on asymptotic expansions for interpolating splines obtained by \textit{T. R. Lucas} [SIAM J. Numer. Anal. 19, 1051-1066 (1982; Zbl 0519.41010)] and the author himself [Sci. Sin., Ser. A 26, 919-930 (1983; Zbl 0524.41006)].
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2017
In this chapter, we relax the homogeneous portfolio assumption, and we derive an asymptotic series expansion of the \(k{\text {th}}\)-to-default Q-factor in the non-homogeneous case. We also show how to compute the conditional aggregate default distributions that appear in the expansion using the convolution recursion algorithm.
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In this chapter, we relax the homogeneous portfolio assumption, and we derive an asymptotic series expansion of the \(k{\text {th}}\)-to-default Q-factor in the non-homogeneous case. We also show how to compute the conditional aggregate default distributions that appear in the expansion using the convolution recursion algorithm.
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