分数布朗运动参数估计

为了估计分形布朗运动参数,作者进一步修改了Wornell算法.克服了Wornell算法要求样本数量大的缺陷.在仿真中,和lance等人修改的Wornell算法相比较,算法达到了更高的精度,并以均方根误差和标准差为指标说明了本文方法的优越性.     

Obtaining equations of motion for charged particles in the (<Emphasis Type="Italic">v/c</Emphasis>)<Superscript>3</Superscript>-approximation by the Einstein-Infeld-Hoffmann method

We consider some principal methodological problems that appear when the Einstein-Infeld-Hoffmann method is used to find approximate solutions of the general relativity equations and to obtain information about the motion of particles whose interaction force is much greater than the gravitational attraction force. Among these problems are normalizing approximate expressions by expanding exact solutions written in the same coordinate conditions used in the Einstein-Infeld-Hoffmann method, assigning the smallness orders depending on relations between the smallness parameters in play, and verifying cancellations of divergent terms arising in surface integrals. Solving these questions in accordance with the internal logic of the Einstein-Infeld-Hoffmann method results in new tools and techniques for applying the method. We demonstrate these tools and techniques in the example of the problem of the motion of two electrically charged pointlike particles in the (v/c)³-approximation.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 160–176, January, 2005.     

Large deviation principle for enhanced Gaussian processes

We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N. We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced (fractional) Brownian motion, in Hölder- or modulus topology, appears as special case.     

Estimates on Green functions and Schrödinger-type equations for non-symmetric diffusions with measure-valued drifts

In this paper, we establish sharp two-sided estimates for the Green functions of non-symmetric diffusions with measure-valued drifts in bounded Lipschitz domains. As consequences of these estimates, we get a 3G type theorem and a conditional gauge theorem for these diffusions in bounded Lipschitz domains.Informally the Schrödinger-type operators we consider are of the form L+μ⋅∇+ν where L is a uniformly elliptic second order differential operator, μ is a vector-valued signed measure belonging to Kd,1 and ν is a signed measure belonging to Kd,2. In this paper, we establish two-sided estimates for the heat kernels of Schrödinger-type operators in bounded C1,1-domains and a scale invariant boundary Harnack principle for the positive harmonic functions with respect to Schrödinger-type operators in bounded Lipschitz domains.     

一种新的运动自适应去隔行算法

提出基于棱边方向检测的运动自适应去隔行算法,该算法能充分利用图像序列的时间和空间上的相关信息,采用新颖的相邻场运动检测方法区分视频序列中的运动和静止部分.对于运动部分,使用改进的基于棱边方向的边沿自适应插值算法;对于静止部分,采用三点中值滤波插值算法.仿真实验表明：算法无论在画面视觉效果还是视频图像信噪比,均达到良好了效果.     

分数布朗运动模型的分维的估计方法(英文)

本文探讨分数布朗运动模型的分维的统计确定问题,给出几种新的估计方法．     

Iterated processes and their applications to higher order differential equations

In this paper we construct models obtained by suitably combining Brownian motions and telegraphs in such a way that their transition functions satisfy higher-order parabolic or hyperbolic equations of different types. Equations with time-varying coefficients are also derived by considering processes endowed either with drift or with suitable modifications of their structure. Finally the distribution of the maximum of the iterated Brownian motion (along with some other properties) is presented. This work is partially supported by the Natural Science Foundation of Guangdong Province, National Natural Science Foundation of China grant No. 19501026 and the Alexander von Humbodlt Foundation     

On retardation,radiation and Liénard–Wiechert type potentials in electrodynamics and elastodynamics

The aim of this paper is to investigate the fundamental problems of retardation and radiation caused by non-uniformly moving point sources using the theories of electrodynamics and elastodynamics. This paper investigates and compares the retarded electromagnetic fields and the retarded elastodynamic fields. For the non-uniform motion of a general point source, the Liénard–Wiechert type potentials and the radiation and nonradiation fields are derived for a point charge and for a point force.     

Design of an Optimal Grid for Finite Element Methods

ABSTRACT Finite element solutions of improved quality are obtained by optimizing the location of nodes of the finite element grid, while keeping the number of degrees of freedom fixed. The formulation of the grid optimization problem is based on the reduction of error associated with interpolation of the exact solution, using functions from the finite element space. Element sizes are selected as design variables: length in R1 and area in R2. Analytically derived optimality conditions are presented and an approximation to these conditions is introduced to obtain a set of operationally useful equations that can be used as guidelines for construction of improved grids. Example problems are given for illustration.     

Estimating the efficient price from the order flow: A Brownian Cox process approach

At the ultra high frequency level, the notion of price of an asset is very ambiguous. Indeed, many different prices can be defined (last traded price, best bid price, mid price, etc.). Thus, in practice, market participants face the problem of choosing a price when implementing their strategies. In this work, we propose a notion of efficient price which seems relevant in practice. Furthermore, we provide a statistical methodology enabling to estimate this price from the order flow.