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Geometric Influences II: Correlation Inequalities and Noise Sensitivity
Influences geometric influences noise sensitivity correlation between increasing sets Talagrand’s bound Gaussian measure isoperimetric inequality
2012/6/25
In a recent paper, we presented a new definition of influences in product spaces of continuous distributions, and showed that analogues of the most fundamental results on discrete influences, such as ...
Connectivity Threshold of Random Geometric Graphs with Cantor Distributed Vertices
Cantor distribution connectivity threshold random geometric graph singular distributions
2012/4/18
For connectivity of \emph{random geometric graphs}, where there is no density for underlying distribution of the vertices, we consider $n$ i.i.d. \emph{Cantor} distributed points on $[0,1]$. We show t...
复合Poisson-Geometric风险模型能够较好地刻画风险事件和赔付事件有可能是不等价的情形，在保险中有其实际应用的背景.研究了重尾索赔下带干扰的复合Poisson-Geometric风险模型，得到破产概率所满足的一个渐近表达式.这个结果在形式上与经典的带扰动的复合Poisson风险模型是一致的.
Potential theory of one-dimensional geometric stable processes
geometric stable process Green function first exit time tail function Poisson kernel Levy process
2011/8/25
Abstract: The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter $\alpha\in(0...
Homomorphisms of abelian varieties over geometric fields of finite characteristic
Homomorphisms of abelian varieties geometric fields of finite characteristic
2011/2/25
We study analogues of Tate’s conjecture on homomorphisms for abelian varieties when the ground field is finitely generated over an algebraic closure of a finite field. Our results cover the case of ab...
Rational term structure models with geometric Levy martingales
Rational term structure models geometric Levy martingales
2011/3/2
In the \positive interest" models of Flesaker and Hughston, the nominal discount bond system is determined by the speci cation of a one-parameter family of positive martingales.
对索赔到达为复合Poisson-Geometric过程的风险模型进行了推广, 研究了带有干扰条件下保单到达为参数α的Poisson过程,运用鞅论的方法得出了多险种风险模型下破产概率满足的Lundberg不等式和一般公式。