Analytic Approximations to GARCH Aggregated Returns Distributions with Applications to VaR and ETL

2011 ◽  
Author(s):  
Carol Alexander ◽  
Emese Lazar ◽  
Silvia Stanescu
Keyword(s):  
Analytic Approximations

Analytic approximations for inside-outside interferometry

1990 ◽  
Vol 339 (2) ◽  
pp. 378-392 ◽  
Author(s):  
Sandra S. Padula ◽  
Miklos Gyulassy
Keyword(s):  
Analytic Approximations

scholarly journals Superoptimal Analytic Approximations of Matrix Functions

1994 ◽  
Vol 120 (2) ◽  
pp. 300-343 ◽  
Author(s):  
V.V. Peller ◽  
N.J. Young
Keyword(s):  
Matrix Functions ◽  
Analytic Approximations

Splitting of Separatrices in the Rapidly Forced Duffing Oscillator

1993 ◽  
Author(s):  
Alexander F. Vakakis
Keyword(s):  
Asymptotic Approximation ◽  
Duffing Oscillator ◽  
Perturbation Parameter ◽  
Negative Stiffness ◽  
Stable And Unstable Manifolds ◽  
Analytic Approximations ◽  
Melnikov Integral ◽  
Unstable Manifolds ◽  
Splitting Of Separatrices ◽  
Splitting Distance

Abstract The splitting of the stable and unstable manifolds of the rapidly forced Duffing oscillator with negative stiffness is investigated. The method used relies on the computation of analytic approximations for the orbits on the perturbed manifolds, and the asymptotic approximation of these orbits by successive integrations by parts. It is shown, that the splitting of the manifolds becomes exponentially small as the perturbation parameter tends to zero, and that the estimate for the splitting distance given by the Melnikov Integral dominates over high order corrections.

Sign in / Sign up

Export Citation Format

Share Document