随机市场系数的M-V最优投资组合选择:一个鞅方法

通过引进凹函数U(x)以及等价鞅测度p^-，应用鞅的性质得到了随机市场系数情形下的M—V模型的最优投资策略以及有效前沿．     

On some measures and distances for positive random variables

A number of conventional measures of risk as real‐valued functions on the space of positive random variables are considered: the expected shortfall, the mean excess over the threshold, the stop‐loss and some others. Ordering of risks, based on these measures and the distances between corresponding distribution functions, are described. The perturbed measures, describing the effect of changing environment, are discussed. These measures are defined by the accelerated life and proportional hazards models widely used in reliability and survival analysis. The case of a random environment is of a prime interest in the paper. The main result states that if, for instance, the stochastic environment is ‘neutral in expectation’ with respect to the baseline one, the distance between the corresponding distribution functions can be still sufficiently large. Copyright © 2003 John Wiley & Sons, Ltd.     

Janossy Densities. II. Pfaffian Ensembles

We extend the main result of the companion paper J. Stat. Phys. 113:595–610 to the case of the pfaffian ensembles.     

关于离散随机变量熵的一个上界

本文分析了离散随机变量熵与方差及有关微分熵的某种关系，给出了离散随机变量熵的一个上界，改进了Ｔ．Ｍ．Ｃｏｖｅｒ与Ｊ．Ａ．Ｔｈｏｍａｓ关于离散熵的上界的已有结果［１］，并以图和表的方式举出一些实例加以比较。     

Multiperiodic multifractal martingale measures

A nonnegative 1-periodic multifractal measure on is obtained as infinite random product of harmonics of a 1-periodic function W(t). Such infinite products are statistically self-affine and generalize certain Riesz products with random phases. They are martingale structures, therefore converge. The criterion on W for nondegeneracy is provided. It differs completely from those for other known random measures constructed as martingale limits of multiplicative processes. In particular, it is very sensitive to small changes in W(t). When these infinite products are interpreted in the framework of thermodynamic formalism for random transformations, logW is a potential function when W>0. For regular enough potentials, in case of degeneracy, the natural normalization makes the sequence of measures converge. Moreover, this normalization is neutral for nondegenerate martingales. The multifractal analysis of the limit martingale measure is performed for a class of potential functions having a dense countable set of jump points.     

On the asymmetric clocked buffered switch

A 2 × 2 clocked buffered switch is a device used in data-processing networks for routing messages from one node to another. The message handling process of this switch can be modelled as a two-server, time slotted, queueing process with state space the number of messages (x_n , y_n) present at the servers at the end of a time slot. The x_n , y_n-process is a two-dimensional nearest-neighbour random walk. In the present study the bivariate generating function Φ(p,q) of the stationary distribution of this random walk is determined, assuming that this distribution exists. Φ(p,q) is known, whenever Φ(p,0) and Φ(0,q) are known. The essential points of the present study are the construction of these two functions from the knowledge of their poles and zeros and the simple determination of these poles and zeros. This revised version was published online in June 2006 with corrections to the Cover Date.     

二维随机粗糙面的fBm模拟及其统计特性

数值模拟在物理建模中具有相当重要的地位。本文基于对二维分形布朗运动（ｆＢｍ）的研究，根据ｆＢｍ的特征，阐述了用二维ｆＢｍ函数模拟随机粗糙面的方法。由于很多电磁散射问题与粗糙面的各阶矩有很大的关系，我们导出了二维随机粗糙面的统计参量与分维Ｄ的关系。基于对二维ｆＢｍ的小波分析，提出了在时－频相空间估计分维Ｄ的方法。这种方法比较简单而切实可行，不但适合于粗糙面整体分维的计算，更适合于局部分数维的计算。所     

Hitting time of large subsets of the hypercube

We study the simple random walk on the n‐dimensional hypercube, in particular its hitting times of large (possibly random) sets. We give simple conditions on these sets ensuring that the properly rescaled hitting time is asymptotically exponentially distributed, uniformly in the starting position of the walk. These conditions are then verified for percolation clouds with densities that are much smaller than (n log n)^‐1. A main motivation behind this article is the study of the so‐called aging phenomenon in the Random Energy Model, the simplest model of a mean‐field spin glass. Our results allow us to prove aging in the REM for all temperatures, thereby extending earlier results to their optimal temperature domain. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Ising models on hyperbolic graphs

We consider Ising models on a hyperbolic graph which, loosely speaking, is a discretization of the hyperbolic planeH ² in the same sense asZ ^d is a discretization ofR ^d . We prove that the models exhibit multiple phase transitions. Analogous results for Potts models can be obtained in the same way.