一些次线性算子在非齐性弱Herz空间中的有界性

本文在具有仅满足增长性条件测度μ的非齐性空间上引入了弱H erz空间,并讨论了某些次线性算子在该空间上的有界性;特别的,我们得到了分数次积分算子的有界性.     

Some Useful Integral Representations for Information-Theoretic Analyses

This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact formulas for quantities that involve expectations of the logarithm of a positive random variable. Here, in the same spirit, we derive an exact integral representation (in one or two dimensions) of the moment of a nonnegative random variable, or the sum of such independent random variables, where the moment order is a general positive non-integer real (also known as fractional moments). The proposed formula is applied to a variety of examples with an information-theoretic motivation, and it is shown how it facilitates their numerical evaluations. In particular, when applied to the calculation of a moment of the sum of a large number, n, of nonnegative random variables, it is clear that integration over one or two dimensions, as suggested by our proposed integral representation, is significantly easier than the alternative of integrating over n dimensions, as needed in the direct calculation of the desired moment.     

Closed‐form approximations for spread options in Lévy markets

We provide new closed‐form approximations for the pricing of spread options in three specific instances of exponential Lévy markets, ie, when log‐returns are modeled as Brownian motions (Black‐Scholes model), variance gamma processes (VG model), or normal inverse Gaussian processes (NIG model). For the specific case of exchange options (spread options with zero strike), we generalize the well‐known Margrabe formula (1978) that is valid in a Black‐Scholes model to the VG model under a homogeneity assumption.     

Expectation of intrinsic volumes of random polytopes

Let K be a convex body in ℝ ^d , let j ∈ {1, …, d−1}, and let K(n) be the convex hull of n points chosen randomly, independently and uniformly from K. If ∂K is C ₊², then an asymptotic formula is known due to M. Reitzner (and due to I. Bárány if ∂K is C ₊³) for the difference of the jth intrinsic volume of K and the expectation of the jth intrinsic volume of K(n). We extend this formula to the case when the only condition on K is that a ball rolls freely inside K. Funded by the Marie-Curie Research Training Network “Phenomena in High-Dimensions” (MRTN-CT-2004-511953).     

Optimal approximations for risk measures of sums of lognormals based on conditional expectations

In this paper we investigate the approximations for the distribution function of a sum S$S$ of lognormal random variables. These approximations are obtained by considering the conditional expectation E[S∣Λ]$E[S\mid \Lambda ]$ of S$S$ with respect to a conditioning random variable Λ$\Lambda$.     

一类分数次积分算子在Herz型Hardy空间上的有界性

通过放宽尺寸条件,得到了一类具有分数次积分性质的次线性算子从Herz型Hardy空间到(弱)Herz型Hardy空间有界性的判定条件,以及端点处的弱型估计.     

基于随机效应Wiener退化模型的剩余寿命预测

针对退化率较高的产品具有不稳定的退化路径以及产品个体差异对退化过程的影响,建立了一种新的随机效应退化模型,即漂移参数和扩散参数均为随机变量且两者之间呈线性关系的Wiener退化过程模型.基于该模型获得了产品剩余寿命分布与可靠度函数,同时设计了估计模型参数的EM（expectation maximization）算法.最后,通过分析钛合金疲劳裂纹数据以及与现有模型结果的比较,验证了所建模型的有效性和准确性.