Higher-Order Laplace Equations and Hyper-Cauchy Distributions

On the Cauchy problem for higher-order nonlinear dispersive equations

We study the higher-order nonlinear dispersive equation ∂tu+ ∂ 2j+1 x u = ∑ 0≤j1+j2≤2j aj1,j2∂ j1 x u∂ j2 x u, x, t ∈ R. where u is a real(or complex-) valued function. We show that the associated initial value problem is well posed in weighted Besov and Sobolev spaces for small initial data. We also prove ill-posedness results when a0,k 6= 0 for some k > j, in the sense that this equation cann...

Asymmetric Univariate and Bivariate Laplace and Generalized Laplace Distributions

Alternative specifications of univariate asymmetric Laplace models are described and investigated. A more general mixture model is then introduced. Bivariate extensions of these models are discussed in some detail, with particular emphasis on associated parameter estimation strategies. Multivariate versions of the models are briefly introduced.

Higher Order Laplace Integration and the Hyper-accuracy of Recent Likelihood Methods

SUMMARY We develop a third order approximation for the distribution function of an asymptotic density function on the real line with a scalar parameter; a computer implementation is available on the web. The derivation makes use of integration that is obtained by symbolic computer algebra. In applications, information of various kinds may be available concerning a density function and its normi...

Fuzzy laplace transform on two order derivative and solving fuzzy two order differential equations

Higher Order Cauchy Problems in Bounded Domains

Abstract. We study solutions of a class of higher order partial differential equations in bounded domains. These partial differential equations appeared first time in the papers of Baeumer, Meerschaert and Nane [10] and Meerschaert, Nane and Vellaisamy [31], and Nane [36]. We express the solutions by subordinating a killed Markov process by a hitting time of a stable subordinator of index 0 < β...