MENCARI RESIDU UNTUK MENCARI TRANSFORMASI LAPLACE INVERS

Laplace transform represent one of used mathematics component in many other science. This, \ud because Laplace transform give effective and easy method to get solution from various problem. \ud Application of Residu can be used to look for Laplace invers transform at singular of function . \ud By using formula of complex invers can give easy solution in searching Laplace invers \ud transform, that is by using contour Bromwich and integral contour, hence solution of Laplace \ud invers transform directly earn in searching by using application of residu for function singularity. \ud By using formula of invers complex, hence resolving of Laplace invers transforms by using \ud method of residu can be conducted. This writing will develop and depict Application of residu to \ud look for Laplace invers transform at polar dot singularity, singularity which to the number of do \ud not till, and branch poin

Efficient pricing options under regime switching

In the paper, we propose two new efficient methods for pricing barrier option in wide classes of Lévy processes with/without regime switching. Both methods are based on the numerical Laplace transform inversion formulae and the Fast Wiener-Hopf factorization method developed in Kudryavtsev and Levendorski\v{i} (Finance Stoch. 13: 531--562, 2009). The first method uses the Gaver-Stehfest algorithm, the second one -- the Post-Widder formula. We prove the advantage of the new methods in terms of accuracy and convergence by using Monte-Carlo simulations.Lévy processes; barrier options;regime switching models; Wiener-Hopf factorization; Laplace transform; numerical methods; numerical transform inversion

Generalized Post-Widder inversion formula with application to statistics

In this work we derive an inversion formula for the Laplace transform of a density observed on a curve in the complex domain, which generalizes the well known Post-Widder formula. We establish convergence of our inversion method and derive the corresponding convergence rates for the case of a Laplace transform of a smooth density. As an application we consider the problem of statistical inference for variance-mean mixture models. We construct a nonparametric estimator for the mixing density based on the generalized Post-Widder formula, derive bounds for its root mean square error and give a brief numerical example

A modal approach for the solution of the non-linear induction problem in ferromagnetic media

The non-linear induction problem in ferromagnetic media is solved using the fixed-point iteration method, where the linearized problem at each iteration is treated by means of a modal approach. The proposed approach does not require meshing of the solution domain, which results in fast computations comparing to conventional mesh-based numerical techniques. Both harmonic and pulse excitations are considered via Fourier and Laplace transform, respectively. An efficient method for the fast computation of the inverse Laplace transform of the magnetic polarization signals is also devised based on the generalized pencil-of-function (GPOF) method. Although being restricted to one dimensional configurations, the present work provide the tools for the treatment of two and three dimensional problems, whose study is under way

Tail bounds for all eigenvalues of a sum of random matrices

This work introduces the minimax Laplace transform method, a modification of the cumulant-based matrix Laplace transform method developed in "User-friendly tail bounds for sums of random matrices" (arXiv:1004.4389v6) that yields both upper and lower bounds on each eigenvalue of a sum of random self-adjoint matrices. This machinery is used to derive eigenvalue analogues of the classical Chernoff, Bennett, and Bernstein bounds. Two examples demonstrate the efficacy of the minimax Laplace transform. The first concerns the effects of column sparsification on the spectrum of a matrix with orthonormal rows. Here, the behavior of the singular values can be described in terms of coherence-like quantities. The second example addresses the question of relative accuracy in the estimation of eigenvalues of the covariance matrix of a random process. Standard results on the convergence of sample covariance matrices provide bounds on the number of samples needed to obtain relative accuracy in the spectral norm, but these results only guarantee relative accuracy in the estimate of the maximum eigenvalue. The minimax Laplace transform argument establishes that if the lowest eigenvalues decay sufficiently fast, on the order of (K^2*r*log(p))/eps^2 samples, where K is the condition number of an optimal rank-r approximation to C, are sufficient to ensure that the dominant r eigenvalues of the covariance matrix of a N(0, C) random vector are estimated to within a factor of 1+-eps with high probability.Comment: 20 pages, 1 figure, see also arXiv:1004.4389v

Solutions of linear multi-dimensional fractional order Volterra integral equations

In this paper, the aim studying this topic is to extend the study of the one-dimensional fractional to the multi-dimensional fractional integral equations and their applications. The multi-dimensional Laplace transform method (M.D.L.T.M) is developed to solve multi-dimensional fractional Integrals equations. We used the one-dimensional Laplace transform for solving the fractional integral. The procedure will simply to find the Laplace transform to the equation, to solve the transform of the unknown function. Finally, find the inverse Laplace to obtain our desired solution. The result reveals that the transform method is very convenient and effective