分形多孔介质中的奇异扩散

分形多孔介质和均质多孔介质相比具有许多特殊的性质,它在各个不同的尺度上有相互钳套的自相似结构.孔隙分形中的粒子扩散和经典的Fick扩散不同,其均方位移服从分形幂律关系.据此对孔隙分形中的粒子扩散利用随机过程的统计方法建立了奇异扩散的理论模型,讨论了奇异扩散的非马尔可夫性质和分形性质.     

随机环境中有界跳幅的分枝随机游动

考虑随机环境中有界跳幅的分枝随机游动,其中粒子的繁衍构成时间随机环境中的分枝过程,粒子的运动遵循空间随机环境中有界跳幅的随机游动规律.在分枝过程不灭绝的条件下,文章研究n时刻最右粒子位置的极限性质.     

模糊二阶矩过程及均方收敛性

基于可信性测度,定义了新的模糊二阶矩过程,证明了该二阶矩过程存在方差函数和协方差函数.对于在可信性空间(Θ,()(Θ),Cr)上具有二阶矩的模糊变量集合H,证明了其对通常的线性运算封闭,并在H中研究了模糊均方收敛的必要条件和充分条件.最后讨论了模糊均方收敛的若干性质.     

随机微分方程大偏差的一个稳定性结论及其应用

本文证明了对可能退化的扰动泛函型随机微分方程,其漂移项增加适当的扰动不改变大偏差性质。该结果应用于漂移系数在一个超曲面上跳跃的退化扩散过程。     

球面介质作用下的测度值分枝过程

我们考虑空间上一粒子系统，当其受到分布于求面上的介质作进行粒子分枝和衍生，产生新了体，而新粒子仍按原粒子的运动规则继续空间运动。通过合理的假设和极限过程，粒子在空间的散布一测度值分枝过程来刻划。     

非Lipschitz条件下高维McKean-Vlasov随机微分方程解的存在唯一性

研究了一类漂移系数不连续的高维McKean-Vlasov随机微分方程及相应的粒子系统解的存在唯一性.在漂移系数关于空间变量逐段Lipschitz连续的条件下，首先利用Zvonkin变换将方程转换为漂移系数为Lipschitz连续的McKean-Vlasov随机微分方程，变换后的方程存在唯一解.然后由变换函数的性质可得逆函数的存在性和Lipschitz连续性.最后由It8公式及逆函数的性质可得原来的McKean-Vlasov随机微分方程及相应的粒子系统解的存在唯一性.     

推广Einstein场方程为随机微分方程

在这篇论文中,我们推广了Einstein场方程成为随机微分方程: 其几何张量和物质张量的分量都被约定为均方连续和均方可微的随机函数。 我们得以建立一些非常深刻的新观点: a.随机Einstein场方程表示随机物质源决定着空-时的随机结构。这一方程的均方解——均方可微的随机度规函数表征着一类随机空-时微分流形。 b.这类随机空-时微分流形可以解释为浸没在R~n空间中的随机超曲面S。在S中任意运动(包括随机运动)的坐标变换下,ds~2是不变量;而且,物理方程也具有协变性,我们称之为随机协变原理。 c.我们解出了这一随机Einstein场方程的一个特殊的均方解(见§4之(18)式)。     

基于PSO-AFSA混合算法的模糊投资组合问题的研究

针对模糊不确定的证券市场,用可能性均值、下可能性方差和协方差分别替换了投资组合模型中概率均值、方差和协方差,构建了双目标均值-方差投资组合模型。然后采用线性加权法将双目标模型转化为单目标模型,进而提出了一个PSO-AFSA混合算法对其求解。该混合算法中,将粒子群算法搜索的结果作为人工鱼群算法初始鱼群,进一步搜索,这样能有效的避免粒子群算法陷入局部最优。同时,将人工鱼群中的最好位置反馈到粒子群算法的速度更新公式中,指引粒子运动,加快算法收敛。最后,进行实例分析,结果表明:PSO-AFSA混合算法是有效的,混合算法搜索到的全局最优值好于基本粒子群算法搜索到的全局最优值。     

一类连续状态非线性分枝过程的离散逼近

本文考虑一类连续状态非线性分枝过程.直观上,这是一类带竞争且分枝速率与状态相依的连续状态分枝过程.我们可以用由Brown运动和Poisson随机测度驱动的随机微分方程的解来构造该类过程.本文的主要结果是构造一列离散状态Markov链,并在较弱的条件下,通过胎紧性结论以及构造无穷维乘积空间上的收敛序列的方法证明其在轨道空间上弱收敛于上述连续状态的非线性分枝过程.     

基于加速梯度算法的高维协方差矩阵估计的研究

稀疏性和正定性是高维稀疏协方差矩阵估计中要保证的两个重要性质.为了保证这两个性质被高效的实现,我们使用一个正定的l₁惩罚来估计高维协方差矩阵,并使用一个有竞争力的加速梯度算法去实现估计.实验结果表明,与其他方法相比,该方法在计算时间、正确率、错误率、F范数等指标上具有较好的表现,同时实现了最优解达到O(1/k~2)的收敛速率.     

SPDE with generalized drift and fractional-type noise

We consider a stochastic partial differential equation involving a second order differential operator whose drift is discontinuous. The equation is driven by a Gaussian noise which behaves as a Wiener process in space and the time covariance generates a signed measure. This class includes the Brownian motion, fractional Brownian motion and other related processes. We give a necessary and sufficient condition for the existence of the solution and we study the path regularity of this solution.     

Some Invariance Principles for Random Vectors in the Generalized Domain of Attraction of the Multivariate Normal Law

For independent identically distributed random vectors belonging to the generalized Domain of Attraction of the multivariate normal law, we define two partial sum processes analogous to that of Donsker's Theorem. We prove that each converges in distribution to a Brownian Motion in the space of continuous functions. One process uses nonrandom operator normalization, and the other is a studentization of the first, using normalization by the empirical covariance operator.     

Rescaled contact processes converge to super-Brownian motion in two or more dimensions

We show that in dimensions two or more a sequence of long range contact processes suitably rescaled in space and time converges to a super-Brownian motion with drift. As a consequence of this result we can improve the results of Bramson, Durrett, and Swindle (1989) by replacing their order of magnitude estimates of how close the critical value is to 1 with sharp asymptotics. Received: 2 February 1998 / Revised version: 28 August 1998     

On the Gaussian fluctuations of the critical Curie-Weiss model in statistical mechanics

Summary It has been known for some time that the fluctuations of the Curie-Weiss mean field model of ferromagnetism are non-Gaussian at the critical temperature. Here we establish the presence of a substantial Gaussian element in the critical model by showing that the internal fluctuations, i.e. the fluctuations within the fluctuating field, are Gaussian. We show for instance that, as the number n of sites increases to infinity, the system, with the appropriate space and spin scalings, behaves asymptotically as a Brownian motion with randomised drift, and that the distribution of the drift has the non-Gaussian form familiar in this theory. With the more conventional space scaling 1/n it is known that the system degenerates asymptotically to a straight line with random slope. We prove here that the error from the straight line, when appropriately amplified, converges in distribution to a Brownian bridge.Dedicated to Klaus Krickeberg on the occasion of his 60th birthday     

A new approach to stochastic evolution equations with adapted drift

In this paper we develop a new approach to stochastic evolution equations with an unbounded drift A which is dependent on time and the underlying probability space in an adapted way. It is well-known that the semigroup approach to equations with random drift leads to adaptedness problems for the stochastic convolution term. In this paper we give a new representation formula for the stochastic convolution which avoids integration of non-adapted processes. Here we mainly consider the parabolic setting. We establish connections with other solution concepts such as weak solutions. The usual parabolic regularity properties are derived and we show that the new approach can be applied in the study of semilinear problems with random drift. At the end of the paper the results are illustrated with two examples of stochastic heat equations with random drift.     

Théorème limite pour une équation différentielle à coefficient aléatoire à mémoire longue

We consider an ordinary differential equation depending on a small parameter and with a long-range random coefficient. We establish that the solution of this ordinary differential equation converges to the solution of a stochastic differential equation driven by a fractional Brownian motion. The index of the fractional Brownian motion depends on the asymptotic behavior of the covariance function of the random coefficient. The proof of the convergence uses the T. Lyons theory of “rough paths”. To cite this article: R. Marty, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Stochastic Description of a Bose�CEinstein Condensate

In this work we give a positive answer to the following question: does Stochastic Mechanics uniquely define a three-dimensional stochastic process which describes the motion of a particle in a Bose?CEinstein condensate? To this extent we study a system of N trapped bosons with pair interaction at zero temperature under the Gross?CPitaevskii scaling, which allows to give a theoretical proof of Bose?CEinstein condensation for interacting trapped gases in the limit of N going to infinity. We show that under the assumption of strictly positivity and continuous differentiability of the many-body ground state wave function it is possible to rigorously define a one-particle stochastic process, unique in law, which describes the motion of a single particle in the gas and we show that, in the scaling limit, the one-particle process continuously remains outside a time dependent random ??interaction-set?? with probability one. Moreover, we prove that its stopped version converges, in a relative entropy sense, toward a Markov diffusion whose drift is uniquely determined by the order parameter, that is the wave function of the condensate.     

Large deviations and exponential decay for the magnetization in a Gaussian random field

Summary. We consider a continuous model for transverse magnetization of spins diffusing in a homogeneous Gaussian random longitudinal field , where is the coupling constant giving the intensity of the random field. In this setting, the transverse magnetization is given by the formula , where is the standard process of Brownian motion and is the covariance function of the original random field . We use large deviation techniques to show that the limit exists. We also determine the small behavior of the rate and show that it is indeed decaying as conjectured in the physics literature. Received: 30 June 1995 / In revised form: 26 January 1996     

The Approach to the Covariance of the Outer Producter of Two Independent Random Vector in Inter Productor Space

The purpose of this article is to prescnt by using vector space methods. a formula as how to calculate the covariance of the outer product of two independent random vecters in inter product space and to makes a discussion on the covariance of the orthogonally invariant random vector and that of the weakly spherically distributed orter produt.     

On optimal investment with processes of long or negative memory

We consider the problem of utility maximization for investors with power utility functions. Building on the earlier work Larsen et al. (2016), we prove that the value of the problem is a Fréchet-differentiable function of the drift of the price process, provided that this drift lies in a suitable Banach space.We then study optimal investment problems with non-Markovian driving processes. In such models there is no hope to get a formula for the achievable maximal utility. Applying results of the first part of the paper we provide first order expansions for certain problems involving fractional Brownian motion either in the drift or in the volatility. We also point out how asymptotic results can be derived for models with strong mean reversion.