Parametric modeling of third-order cumulant sequences has assumed importance recently because of the applications of the bispectrum. Approaches have been developed for autoregressive modeling of random processes using third-order cumulants, and these are based on solving linear equations which a re necessary but not sufficient conditions for matching samples of the cumulant sequence of the mode...

Geological formations are ubiquitously heterogeneous, and the equations that govern flow and transport in such formations can be treated as stochastic partial differential equations. The Monte Carlo method is a straightforward approach for simulating flow in heterogeneous porous media; an alternative based on the moment-equation approach has been developed in the last two decades to reduce the ...

[1] We consider the numerical prediction of transient flow in bounded, randomly heterogeneous porous media driven by random sources, initial heads, and boundary conditions without resorting to Monte Carlo simulation. After applying the Laplace transform to the governing stochastic flow equations, we derive exact nonlocal (integrodifferential) equations for the mean and variance-covariance of tr...

The closure conditions, which make a finite set of moment equations equivalent to the collisionless Boltzmann equation, are investigated for Gaussian and ellipsoidal velocity distributions working from the complete mathematical expression for the n-order stellar hydrodynamic equation, which was explicitly obtained depending on the comoving moments in a previous paper. First, for a Schwarzschild...

Parametric modeling of third-order cumulant sequences has assumed importance recently because of the applications of the bispectrum. Approaches have been developed for autoregressive modeling of random processes using third-order cumulants, and these are based on solving linear equations which a re necessary but not sufficient conditions for matching samples of the cumulant sequence of the mode...

In the stochastic description of biochemical reaction systems, the time evolution of statistical moments for species population counts is described by a linear dynamical system. However, except for some ideal cases (such as zero- and first-order reaction kinetics), the moment dynamics is underdetermined as lower-order moments depend upon higher-order moments. Here, we propose a novel method to ...

We consider asymptotic approximations to joint posterior distributions in situations where the full conditional distributions referred to in Gibbs sampling are asymptotically normal. Our development focuses on problems where data augmentation facilitates simpler calculations, but results hold more generally. Asymptotic mean vectors are obtained as simultaneous solutions to fixed point equations...

The set of generalized 13 moment equations for molecules interacting with power law potentials [Struchtrup, Multiscale Model. Simul. 3:211 (2004)] forms the base for an investigation of expansion methods in the Knudsen number and other scaling parameters. The scaling parameters appear in the equations by introducing dimensionless quantities for all variables and their gradients. Only some of th...

The numerical simulation of electromagnetic fields is a frequent and time-consuming task in many applications. The behavior of electromagnetic fields is typically described by the timedomain Maxwell equations of first order. These lead to large-scale time-dependent partial differential equations in three spatial dimensions. Often one is only interested in the input-output properties of this sys...

The exact mathematical expression for an arbitrary n-order stellar hydrodynamic equation is explicitly obtained depending on the central moments of the velocity distribution. In such a form the equations are physically meaningful, since they can be compared with the ordinary hydrodynamic equations of compressible, viscous fluids. The equations are deduced without any particular assumptions abou...