Using key tools such as Itô’s formula for general semimartingales, Kunita’s moment estimates for Lévy-type stochastic integrals, and the exponential martingale inequality, we find conditions under which the solutions to the stochastic differential equations (SDEs) driven by Lévy noise are stable in probability, almost surely and moment exponentially stable. Keywords; stochastic differential equ...

The maximum entropy (M.E.) approach to the nite Hausdorr moment problem is studied, a new approach to prove the necessary and suucient conditions for the existence of M.E. solution is considered by transforming the moment problem into a system of ordinary diierential equations. The new technique allows also to prove entropy convergence of the resulting sequence of maximum entropy extimators, an...

Methods to derive macroscopic transport equations for rarefied gases from the Boltzmann equations are presented. Featured methods include the Chapman-Enskog expansion, Grad’s moment method, and the author’s order of magnitude method. The resulting macroscopic equations are compared and discussed by means of simple problems, including linear stability, shock wave structures, and Couette flow.

We discuss a hyperbolic aspect of magnetostriction. The equations governing the longitudinal motion consist of the nonlinear wave equations and the rate equations for the motion of spin for the magnetic moment. We show that the breakdown of smooth solutions will take place in finite time even if the initial data are smooth.

The \closure problem" is a well known and widely discussed problem in transport theory. From the full transport equation one can derive a (innnite) sequence of hyperbolic subsystems for the moments. The question arises how to close the system for the rst n moments. In case of Boltzmann equations it can be answered in the theory of extended thermodynamics. Here we consider transport equations wh...

Abstract. We propose a positive-preserving moment closure for linear kinetic transport equations based on a filtered spherical harmonic (FPN ) expansion in the angular variable. The recently proposed FPN moment equations are known to suffer from the occurrence of (unphysical) negative particle concentrations. The origin of this problem is that the FPN approximation is not always positive at the...

We study the mixed formulation of the stochastic Hodge–Laplace problem defined on an n-dimensional domain D (n 1), with random forcing term. In particular, we focus on the magnetostatic problem and on the Darcy problem in the three-dimensional case. We derive and analyse the moment equations, that is, the deterministic equations solved by the mth moment (m 1) of the unique stochastic solution o...

A wide range of econometric and statistical models are specified through moment conditions. Efficient estimation of such models essentially employs two distinct ideas: optimally combining estimation equations (e.g., the optimal estimating equations of Godambe (1976), the generalized method of moments of Hansen (1982) and the empirical likelihood of Qin and Lawless (1994)), and optimally combini...

The nonlocal hydrodynamic moment equations for compressible convection are compared to numerical simulations. Convective and radiative flux typically deviate less than 20% from the three-dimensional simulations, while mean thermodynamic quantities are accurate to at least 2% for the cases we have investigated. The moment equations are solved in minutes rather than days as required on standard w...

The theoretical studies conducted mainly by the author are reviewed on (1) derivation of arbitrary order moment equations and solutions of some equations, (2) scattering by many particles and the effective medium constant of random medium, (3) scattering by a conducting body in random media and (4) spatially partially-coherent wave scattering, with application to satellite communications, artif...