Dynamic Monte Carlo study on the probability distribution functions of tail-like polymer chain

The configurational properties of tail-like polymer chains with one end attached to a flat surface are studied by using dynamic Monte Carlo technique. We find that the probability distribution of the free end in z direction P(Rz) and the density profile ρ(z) can be scaled approximately by a factor β to be a length independent function for both random walking (RW) and self-avoiding walking (SAW) tail-like chains, where the factor β is related to the mean square end-to-end distance <R2>. The scaled P(Rz) of the SAW chain roughly overlaps that of the RW chain, but the scaled ρ(z) of the SAW chain locates at smaller βz than that of the RW chain.

Estimates for the ruin probability of a time-dependent renewal risk model with dependent by-claims

Consider a continuous-time renewal risk model, in which every main claim induces a delayed by-claim. Assume that the main claim sizes and the inter-arrival times form a sequence of identically distributed random pairs, with each pair obeying a dependence structure, and so do the by-claim sizes and the delay times. Supposing that the main claim sizes with by-claim sizes form a sequence of dependent random variables with dominatedly varying tails, asymptotic estimates for the ruin probability of the surplus process are investigated, by establishing a weakly asymptotic formula, as the initial surplus tends to infinity.

The finite-time ruin probability in the presence of Sarmanov dependent financial and insurance risks

Consider a discrete-time insurance risk model. Within period i, i≥ 1, Xi and Yi denote the net insurance loss and the stochastic discount factor of an insurer, respectively. Assume that {（Xi, Yi）, i≥1） form a sequence of independent and identically distributed random vectors following a common bivariate Sarmanov distribution. In the presence of heavy-tailed net insurance losses, an asymptotic formula is derived for the finite-time ruin probability.

PRECISE RATES IN THE LAW OF THE ITERATED LOGARITHM FOR R/S STATISTICS

Let{Xn;n≥1}be a sequence of i.i.d, random variables with finite variance,Q（n）be the related R/S statistics. It is proved that lim ε↓0 ε^2 ∑n=1 ^8 n log n/1 P{Q（n）≥ε√2n log log n}=2/1 EY^2,where Y=sup0≤t≤1B（t）-inf0≤t≤sB（t）,and B（t） is a Brownian bridge.

PRECISE RATE IN THE LAW OF ITERATED LOGARITHM FOR ρ-MIXING SEQUENCE

Let {X,X n;n≥1} be a strictly stationary sequence of ρ-mixing random variables with mean zero and finite variance. Set S n=n k=1X k,M n=max k≤n｜S k｜,n≥1. Suppose lim n→∞ES2 n/n=∶σ2>0 and ∞n=1ρ 2/d(2n)<∞, where d=2,if -1<b<0 and d>2(b+1),if b≥0. It is proved that,for any b>-1, limε0ε 2(b+1)∞n=1(loglogn)bnlognP{M n≥εσ2nloglogn}= 2(b+1)πГ(b+3/2)∞k=0(-1)k(2k+1) 2b+2,where Г(·) is a Gamma function.

A NOTE ON ASYMPTOTIC BEHAVIOR FOR NEGATIVE DRIFT RANDOM WALK WITH DEPENDENT HEAVY-TAILED STEPS AND ITS APPLICATION TO RISK THEORY

In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process. Xn=-u＋∑j=-∞^∞ φn-jεj, where { ε, εn; -∞〈n〈＋∞} is a sequence of independent, identically distributed random variables with zero mean, u 〉 0 is a constant and the coefficients {φi; -∞〈i〈∞} satisfy 0〈 ∑j=-∞^∞ ｜jφj｜〈 ∞ . Under the conditions that the distribution function of ｜ε｜ has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{sup n≥0 （-qu＋∑j=-∞^∞ εj βnj）〉x} is discussed. Then the result is applied to ultimate ruin probability.

Locally and globally uniform approximations for ruin probabilities of a nonstandard bidimensional risk model with subexponential claims

Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.

基于杂波拖尾分布的雷达无人机检测性能分析

固定翼无人机(unmanned aerial vehicle,UAV)给雷达低空监视提出了严峻挑战。分析雷达对固定翼UAV的检测性能,可为雷达UAV检测能力评估和技术升级提供重要参考。本文结合雷达探测低空固定翼UAV外场实测数据,首先分析了低空固定翼UAV雷达接收信号幅度统计分布,采用多项式对杂波拖尾导致的虚警概率进行拟合建模;然后,根据虚警概率分布得到雷达检测门限;进而根据UAV回波+杂波幅度分布理论推导得到雷达检测概率;最后,将理论分析性能与传统性能分析结果、雷达实际检测性能进行对比。结果表明,采用多项式对杂波拖尾导致的虚警概率进行单独建模,由此获得的雷达检测门限精度更高,从而使雷达UAV检测性能分析结果较传统性能分析结果更准确。

Local asymptotic behavior of the survival probability of the equilibrium renewal model with heavy tails

Recently, Tang established a local asymptotic relation for the ruin probability to the Cram(e)r-Lunbderg risk model.In this short note we extend the corresponding result to the equilibrium renewal risk model.

负二项分布随机变量和尾概率的界

研究了服从不同负二项分布的随机变量和尾概率的界。首先在服从不同负二项分布独立随机变量条件下,利用负二项分布概率母函数和Markov不等式得到了一个随机变量和尾概率的界,并对所求得的界进行改进,获得一个更加精确的界;其次在服从负二项分布的条件下,通过添加相依关系,得到了关于负相依随机变量和尾概率的界。

伽玛分布随机变量和的尾概率界

对服从伽玛分布随机变量和的尾概率界进行了研究,利用伽玛分布的方差和概率母函数对服从伽玛分布随机变量和的尾概率进行估计,从而得到一个随机变量和的尾概率界,并对所求得的界进行改进,获得更加精确的界。在服从伽玛分布的条件下,利用经典的证明方法和一些改进的技术,给出了优化后的尾概率界。

A sharp inequality for the tail probabilities of sums of i.i.d. r.v.'s with dominatedly varying tails

Let F be a distribution function supported on (-∞, ∞) with a finite mean μ. In this note weshow that if its tail F = 1 - F is dominatedly varying, then for any γ＞ max{μ, 0}, there exist C(γ) ＞ 0 and D(γ) ＞ 0 such thatC(γ)nF(x) ≤ Fn*(x) ≤ D(γ)nF(x),for all n ≥ 1 and all x ≥γn. This inequality sharpens a classical inequality for the subexponential distributioncase.

The Finite Time Ruin Probability with the Same Heavy-tailed Insurance and Financial Risks

This note complements a recent study in ruin theory with risky investment byestablishing the same asymptotic estimate for the finite time ruin probability under a weakerrestriction on the financial risks. In particular, our result applies to a critical case that theinsurance and financial risks have Pareto-type tails with the same regular index.

DURATION OF NEGATIVE SURPLUS FOR A TWO STATE MARKOV-MODULATED RISK MODEL

We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.

Ruin Probability and Joint Distributions of Some Actuarial Random Vectors in the Compound Pascal Model

The compound negative binomial model, introduced in this paper, is a discrete time version. We discuss the Markov properties of the surplus process, and study the ruin probability and the joint distributions of actuarial random vectors in this model. By the strong Markov property and the mass function of a defective renewal sequence, we obtain the explicit expressions of the ruin probability, the finite-horizon ruin probability, the joint distributions of T, U（T - 1）, ｜U（T）｜ and inf U（n） （i.e., the time of ruin, the surplus immediately before ruin, the deficit at ruin and maximal deficit from ruin to recovery） and the distributions of some actuarial random vectors.

Asymptotic Ruin Probabilities of the Renewal Model with Constant Interest Force and Dependent Heavy-tailed Claims

在这份报纸，我们为主张相等分布式然而并非必然独立的一个非标准的更新在模型的有限时间、无限时间的毁灭可能性调查 asymptotic 行为。在主张的相同分发属于的假设下面扩大常规变化(ERV ) 的班并且二个主张的联合分布的尾巴与他们的边缘的尾巴相比是可以忽略的，我们为有限时间、无限时间的毁灭可能性获得精确近似。

粒度对重介旋流器分选效果影响的量化解析

分配曲线是重力选煤效果评定的基础,分配曲线形态可用分选密度、可能偏差、四分位偏度、尾态系数4阶特性参数表示,粒度对重选效果的影响可分解成粒度对分配曲线形态参数的影响。以无压三产品重介旋流器在不同粒度下的分配曲线数据为基础,采用基于四分位数的广义正态分布分配曲线数学模型,利用非线性回归方法,分别提取了精煤段和中煤段不同粒级下分配曲线的4阶形态参数,揭示了粒度对无压三产品重介旋流器分选效果影响的基本规律:分选密度随粒度增大先减小后增大,可能偏差随粒度的增大而减小,偏度与尾态系数随粒度增大而趋近于0。即粒度越大,分选精度越高,分配曲线对称性越好,长尾程度越小,分配曲线形态越接近于正态分布。采用幂函数与指数函数相结合的形式,构建了分选密度-粒度数学模型;采用幂函数形式,构建了可能偏差-粒度数学模型;采用幂函数形式,给出了四分位偏差-粒度、尾态系数-粒度数学模型。在4阶形态参数下将重选过程中密度、粒度相互影响统一在基于四分位数的广义正态分布函数中,建立了一个模型参数可扩展的高精度的密度-粒度双变量分配曲面数学模型,为量化分析各类水力分级和重力分选过程粒度密度的相互影响,提供一个通用的数学工具,对于揭示粒度对分选的影响机理具有重要意义。

指数分布的随机变量和的概率不等式

通过对服从指数分布的独立随机变量和的概率不等式的研究,利用指数分布的随机变量的矩母函数与马尔可夫不等式,给出了独立随机变量和的尾概率的界。在给定服从指数分布的独立随机变量和的尾概率的界的基础上,通过在随机变量序列间添加相依结构,得到负相依随机变量和的尾概率的界。

Uniform estimate for maximum of randomly weighted sums with applications to insurance risk theory

This paper obtains the uniform estimate for maximum of sums of independent and heavy-tailed random variables with nonnegative random weights, which can be arbitrarily dependent of each other. Then the applications to ruin probabilities in a discrete time risk model with dependent stochastic returns are considered.

Precise Asymptotics in the Baum-Katz and Davis Laws of Large Numbers of ρ-mixing Sequences

Let {X,Xn;n ≥ 1} be a strictly stationary sequence of ρ-mixing random variables with mean zeros and finite variances. Set Sn =∑k=1^n Xk, Mn=maxk≤n｜Sk｜,n≥1.Suppose limn→∞ESn^2/n=：σ^2〉0 and ∑n^∞=1 ρ^2/d（2^n）〈∞,where d=2 if 1≤r〈2 and d〉r if r≥2.We prove that if E｜X｜^r 〈∞,for 1≤p〈2 and r〉p,then limε→0ε^2（r-p）/2-p ∑∞n=1 n^r/p-2 P{Mn≥εn^1/p}=2p/r-p ∑∞k=1（-1）^k/（2k＋1）^2（r-p）/（2-p）E｜Z｜^2（r-p）/2-p,where Z has a normal distribution with mean 0 and variance σ^2.