Inference in lognormal multidimensional diffusion processes with exogenous factors: Application to modelling in economics

The multidimensional lognormal diffusion process with exogenous factors is treated using the Kolmogorov equations, and the mean vector and covariance matrix are estimated using discrete sampling by the maximum-likelihood method. Also, this process is constructed as a solution of a multidimensional stochastic differential equation, and an estimation is made through the maximum-likelihood method to infer the parameters of the exogenous factors, this time using continuous sampling. Finally, a test for a hypothesis based on these parameters is constructed.     

扩散速度与组元的质量守恒方程*

在混合物流动中,某组元i的质量迁移速度(绝对速度)等于对流速度(牵连速度)与扩散速度(相对速度)之和.扩散速度——以及扩散系数——依对流速度取法之不同而不同.     

A SCATTERING MATRIX MODEL OF SEMICONDUCTOR SUPERLATTICES IN MULTIDIMENSIONAL WAVE—VECTOR SPACE AND ITS DIFFUSION LIMIT

The authors first establish a quantum microscopic scattering matrix model in multidimensional wave-vector space, which relates the phase space density of each superlattice cell with that of the neighbouring cells. Then, in the limit of a large number of cells, a SHE (Spherical Harmonics Expansion)-type model of diffusion equations for the particle number density in the position-energy space is obtained. The crucial features of diffusion constants on retaining the memory of the quantum scattering characteristics of the superlattice elementary cell (like e.g. transmission resonances) are shown in order. Two examples are treated with the analytically computation of the diffusion constants.     

Diffusion relaxation limit of a nonisentropic hydrodynamic model for semiconductors

In this paper, we discussed a general multidimensional nonisentropic hydrodynamical model for semiconductors with small momentum relaxation time. The model is self‐consistent in the sense that the electric field, which forms a forcing term in the momentum equation, is determined by the coupled Poisson equation. With the help of the Maxwell‐type iteration, we prove that, as the relaxation time tends to zero, periodic initial‐value problem of certain scaled multidimensional nonisentropic hydrodynamic model has a unique smooth solution existing in the time interval where the corresponding classical drift‐diffusion model has smooth solutions. Meanwhile, we justify a formal derivation of the drift‐diffusion models from the nonisentropic hydrodynamic models. Copyright © 2007 John Wiley & Sons, Ltd.     

On Castellana–Leadbetter's Condition for Diffusion Density Estimation

A convergence bound is established for the transition density of the ergodic diffusion process. It is known that this condition provides optimality properties for non-parametric estimators of a stationary density.     

A Note on the Transition Density Estimate for Some Diffusion Process on a d–Set

The paper is devoted to transition density estimates for some diffusion process on a d–set. Starting with some local regular Dirichlet form, it is shown, that the associated diffusion satisfies certain upper and lower estimates.      

On Multidimensional Generalized Diffusion Processes

We construct a multidimensional generalized diffusion process with the drift coefficient that is the (generalized) derivative of a vector-valued measure satisfying an analog of the Hölder condition with respect to volume. We prove the existence and continuity of the density of transition probability of this process and obtain standard estimates for this density. We also prove that the trajectories of the process are solutions of a stochastic differential equation.     

On radial stochastic Loewner evolution in multiply connected domains

We discuss the extension of radial SLE to multiply connected planar domains. First, we extend Loewner's theory of slit mappings to multiply connected domains by establishing the radial Komatu-Loewner equation, and show that a simple curve from the boundary to the bulk is encoded by a motion on moduli space and a motion on the boundary of the domain. Then, we show that the vector-field describing the motion of the moduli is Lipschitz. We explain why this implies that “consistent,” conformally invariant random simple curves are described by multidimensional diffusions, where one component is a motion on the boundary, and the other component is a motion on moduli space. We argue what the exact form of this diffusion is (up to a single real parameter κ) in order to model boundaries of percolation clusters. Finally, we show that this moduli diffusion leads to random non-self-crossing curves satisfying the locality property if and only if κ=6.     

Statistical Inference for Student Diffusion Process

We consider the problem of parameter estimation for an ergodic diffusion with the symmetric scaled Student invariant distribution, where the spectral representation of the transition density is given in terms of the finite number of polynomial eigenfunctions (Routh–Romanovski polynomials) and absolutely continuous spectrum of the negative infinitesimal generator of observed diffusion. We prove the consistency and asymptotic normality of the proposed estimators and, based on the Stein equation for Student diffusion, consider the statistical test for the Student distributional assumptions.     

空气中PM2.5的扩散衰减与预测分析

以西安市2013年1月1日-9月19日的空气污染监测数据为例,采用非稳态的二维多箱模型,综合考虑了风向、季节等因素的影响,对西安市PM2.5的面源污染扩散和衰减规律进行模拟预测,计算模型相对误差;再选用高斯模型对某一天西安市突发情况下PM2.5浓度扩散情况进行点源污染扩散预测,并评价模型的有效性.