A Bayesian approach to term structure modeling using heavy‐tailed distributions

In this paper, we introduce a robust extension of the three‐factor model of Diebold and Li (J. Econometrics, 130: 337–364, 2006) using the class of symmetric scale mixtures of normal distributions. Specific distributions examined include the multivariate normal, Student‐t, slash, and variance gamma distributions. In the presence of non‐normality in the data, these distributions provide an appealing robust alternative to the routine use of the normal distribution. Using a Bayesian paradigm, we developed an efficient MCMC algorithm for parameter estimation. Moreover, the mixing parameters obtained as a by‐product of the scale mixture representation can be used to identify outliers. Our results reveal that the Diebold–Li models based on the Student‐t and slash distributions provide significant improvement in in‐sample fit and out‐of‐sample forecast to the US yield data than the usual normal‐based model. Copyright © 2011 John Wiley & Sons, Ltd.     

Asymptotic growth bounds for the 3‐D Vlasov‐Poisson system with point charges

In this article, we consider the asymptotic behavior of the classical solution to the 3‐dimensional Vlasov‐Poisson plasma interacting repulsively with N point charges. The large time behavior in terms of diameters of its velocity‐spatial supports is improved to O(t^2/3+ϵ) for any ϵ>0.     

Asymptotic finite‐time ruin probabilities for a class of path‐dependent heavy‐tailed claim amounts using Poisson spacings

In the compound Poisson risk model, several strong hypotheses may be found too restrictive to describe accurately the evolution of the reserves of an insurance company. This is especially true for a company that faces natural disaster risks like earthquake or flooding. For such risks, claim amounts are often inter‐dependent and they may also depend on the history of the natural phenomenon. The present paper is concerned with a situation of this kind, where each claim amount depends on the previous claim inter‐arrival time, or on past claim inter‐arrival times in a more complex way. Our main purpose is to evaluate, for large initial reserves, the asymptotic finite‐time ruin probabilities of the company when the claim sizes have a heavy‐tailed distribution. The approach is based more particularly on the analysis of spacings in a conditioned Poisson process. Copyright © 2010 John Wiley & Sons, Ltd.     

Global convergence of the Euler‐Poisson system for ion dynamics

We consider smooth solutions of the Euler‐Poisson system for ion dynamics in which the electron density is replaced by a Boltzmann relation. The system arises in the modeling of plasmas, where appear two small parameters, the relaxation time and the Debye length. When the initial data are sufficiently close to constant equilibrium states, we prove the convergence of the system for all time, as each of the parameters goes to zero. The limit systems are drift‐diffusion equations and compressible Euler equations. The proof is based on uniform energy estimates and compactness arguments.     

Long‐time behavior of solution for the compressible Navier‐Stokes‐Maxwell equations in

In this paper, we are concerned with optimal decay rates for higher‐order spatial derivatives of classical solution to the compressible Navier‐Stokes‐Maxwell equations in three‐dimensional whole space. If the initial perturbation is small in ‐norm, we apply the Fourier splitting method to establish optimal decay rates for the second‐order spatial derivatives of a solution. As a by‐product, the rate of classical solution converging to the constant equilibrium state in ‐norm is .     

A fourth‐order Hermitian box‐scheme with fast solver for the Poisson problem in a cube

We present a fourth‐order Hermitian box‐scheme (HB‐scheme) for the Poisson problem in a cube. A single‐nonstaggered regular grid is used supporting the discrete unknowns u and . The scheme is fourth‐order accurate for u and in norm. The fast numerical resolution uses a matrix capacitance method, resulting in a computational complexity of . Numerical results are reported on several examples including nonseparable problems. The present scheme is the extension to the three‐dimensional case of the HB‐scheme presented in Abbas and Croisille [J Sci Comp 49 (2011), 239–267]. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 609–629, 2015     

Robust statistical modeling using the Birnbaum‐Saunders‐t distribution applied to insurance

In this paper, we carry out robust modeling and influence diagnostics in Birnbaum‐Saunders (BS) regression models. Specifically, we present some aspects related to BS and log‐BS distributions and their generalizations from the Student‐t distribution, and develop BS‐t regression models, including maximum likelihood estimation based on the EM algorithm and diagnostic tools. In addition, we apply the obtained results to real data from insurance, which shows the uses of the proposed model. Copyright © 2011 John Wiley & Sons, Ltd.     

Two Tikhonov‐type regularization methods for inverse source problem on the Poisson equation

In this paper, we investigate a problem of the identification of an unknown source on Poisson equation from some fixed location. A conditional stability estimate for an inverse heat source problem is proved. We show that such a problem is mildly ill‐posed and further present two Tikhonov‐type regularization methods (a generalized Tikhonov regularization method and a simplified generalized Tikhonov regularization method) to deal with this problem. Convergence estimates are presented under the a priori choice of the regularization parameter. Numerical results are presented to illustrate the accuracy and efficiency of our methods. Copyright © 2012 John Wiley & Sons, Ltd.     

A new positivity‐preserving nonstandard finite difference scheme for the DWE

An improved positivity‐preserving nonstandard finite difference scheme for the linear damped wave equation is presented. Unlike an earlier such scheme developed by the authors, the new scheme involves three time levels and is therefore able to include the effects of the equation's relaxation coefficient. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential, 2005     

A positivity‐preserving nonstandard finite difference scheme for the damped wave equation

A positivity‐preserving nonstandard finite difference scheme is constructed to solve an initial‐boundary value problem involving heat transfer described by the Maxwell‐Cattaneo thermal conduction law, i.e., a modified form of the classical Fourier flux relation. The resulting heat transport equation is the damped wave equation, a PDE of hyperbolic type. In addition, exact analytical solutions are given, special cases are mentioned, and it is noted that the positivity condition is equivalent to the usual linear stability criteria. Finally, solution profiles are plotted and possible extensions to a delayed diffusion equation and nonlinear reaction‐diffusion systems are discussed. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004.     

Ground state solutions for the nonlinear Schrödinger‐Poisson systems with sum of periodic and vanishing potentials

We study the existence of ground state solutions for the following Schrödinger‐Poisson equations: where is the sum of a periodic potential V_p and a localized potential V_loc and f satisfies the subcritical or critical growth. Although the Nehari‐type monotonicity assumption on f is not satisfied in the subcritical case, we obtain the existence of a ground state solution as a minimizer of the energy functional on Nehari manifold. Moreover, we show that the existence and nonexistence of ground state solutions are dependent on the sign of V_loc.     

Two‐parameter anisotropic homogenization for a Dirichlet problem for the Poisson equation in an unbounded periodically perforated domain. A functional analytic approach

We consider a Dirichlet problem for the Poisson equation in an unbounded periodically perforated domain. The domain has a periodic structure, and the size of each cell is determined by a positive parameter δ, and the level of anisotropy of the cell is determined by a diagonal matrix γ with positive diagonal entries. The relative size of each periodic perforation is instead determined by a positive parameter ε. For a given value of γ, we analyze the behavior of the unique solution of the problem as tends to by an approach which is alternative to that of asymptotic expansions and of classical homogenization theory.     

A direct Schur–Fourier decomposition for the efficient solution of high‐order Poisson equations on loosely coupled parallel computers

In this paper a parallel direct Schur–Fourier decomposition (DSFD) algorithm for the direct solution of arbitrary order discrete Poisson equations on parallel computers is proposed. It is based on a combination of a Direct Schur method and a Fourier decomposition and allows to solve each Poisson equation almost to machine accuracy using only one communication episode. Thus, it is well suited for loosely coupled parallel computers, that have a high network latency compared with the CPU performance. Several three‐dimensional direct numerical simulations (DNS) of wall‐bounded turbulent incompressible flows have been carried out using the DSFD algorithm. Numerical examples illustrating the robustness and scalability of the method on a PC cluster with a conventional 100 Mbits/s network are also presented. Copyright © 2005 John Wiley & Sons, Ltd.     

A Fokas approach to the coupled modified nonlinear Schrödinger equation on the half‐line

In this work, we discuss the coupled modified nonlinear Schrödinger (CMNLS) equation, which describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. By use of the Fokas approach, the initial‐boundary value problem for the CMNLS equation related to a 3×3 matrix Lax pair on the half‐line is to be analyzed. Assuming that the solution {u(x,t),v(x,t)} of CMNLS equation exists, we will prove that it can be expressed in terms of the unique solution of a 3×3 matrix Riemann‐Hilbert problem formulated in the plane of the complex spectral parameter λ. Moreover, we also get that some spectral functions s(λ) and S(λ) are not independent of each other but meet a global relationship.     

A Taylor polynomial approach for solving the most general linear Fredholm integro‐differential‐difference equations

In this study, a matrix method is developed to solve approximately the most general higher order linear Fredholm integro‐differential‐difference equations with variable coefficients under the mixed conditions in terms of Taylor polynomials. This technique reduces the problem into the linear algebraic system. The method is valid for any combination of differential, difference and integral equations. An initial value problem and a boundary value problem are also presented to illustrate the accuracy and efficiency of the method. Copyright © 2012 John Wiley & Sons, Ltd.     

A further study on value distribution of the Riemann zeta‐function

The paper concerns the uniqueness problem of Riemann zeta‐function. It is showed that the Riemann zeta‐function is uniquely determined in terms of the preimages of three complex values except possibly a set G with , where G is called an exceptional set.     

A quasi‐boundary value regularization method for determining the heat source

In this paper, we consider the inverse problem of determining the heat source, which depends only on spatial variable in one‐dimensional heat equation in a bounded domain where data is given at some fixed time. A conditional stability result is given, and a quasi‐boundary value regularization method is also provided. For this regularization solution, the Hölder type stability estimate between the regularization solution and the exact solution is obtained. Numerical examples show that the regularization method is effective and stable. Copyright © 2013 John Wiley & Sons, Ltd.     

A numerical algorithm for the solution of nonlinear fractional differential equations via beta‐derivatives

In this paper, the sinc‐collocation method (SCM) is investigated to obtain the solution of the nonlinear fractional order differential equations based on the relatively new defined fractional derivative, beta‐derivative. For this purpose, a theorem is proved for the approximate solution obtained from the SCM. Moreover, convergence analysis of the SCM is presented. To show the efficiency and the simplicity of the proposed method, some examples are solved, and the results are compared with the exact solutions of the considered equations.