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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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1995
Abstract The following asymptotics related to solutions of the CHE can be studied: Asymptotics of solutions of the CHE in a neighbourhood of the irregular singularity at infinity with special emphasis on Stokes phenomena. Asymptotics of solutions of the CHE and of the monodromy matrices with respect to large values of parameters ...
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Abstract The following asymptotics related to solutions of the CHE can be studied: Asymptotics of solutions of the CHE in a neighbourhood of the irregular singularity at infinity with special emphasis on Stokes phenomena. Asymptotics of solutions of the CHE and of the monodromy matrices with respect to large values of parameters ...
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Normal Approximations and Asymptotic Expansions.
Journal of the American Statistical Association, 1977Marius Iosifescu +2 more
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An Asymptotic Expansion for the Distribution of a Statistic Admitting an Asymptotic Expansion
Theory of Probability & Its Applications, 1973openaire +1 more source