Extremes of Subexponential Shot Noise

Asymptotic behavior of extremes of shot noise in the case of monotone response functions with unbounded support and subexponentially distributed amplitudes is considered. It is assumed that the amplitude distribution belongs to the domain of attraction of a certain maximum-stable law. The limit distribution for maxima is obtained.     

On the Subexponential Property of a Class of Random Variables

Mathematical Notes -     

Asymptotics for Sums of Random Variables with Local Subexponential Behaviour

We study distributions F on [0,) such that for some T , F ^*2(x, x+T] 2F(x, x+T]. The case T = corresponds to F being subexponential, and our analysis shows that the properties for T < are, in fact, very similar to this classical case. A parallel theory is developed in the presence of densities. Applications are given to random walks, the key renewal theorem, compound Poisson process and Bellman–Harris branching processes.     

带有相依重尾冲击的Poisson噪音过程尾的一致渐近性质

本文考虑了带有某种相依重尾冲击的Poisson噪音过程尾的一致渐近性质.当冲击是二元上尾渐近独立的非负随机变量具有长尾和控制变化尾分布且噪音函数具有正的上下界时,得到了过程尾概率的一致渐近公式.进而,当冲击具有连续的一致变化尾分布时,去除了噪音函数具有正的下界的限制.对于噪音函数不一定具有正的上界的情形,当冲击具有两两负象限相依结构时,也得到了一致渐近性结果.     

索赔额服从亚指数分布族S~*的破产概率研究

研究了亚指数分布族中一类特殊的分布,在年索赔额服从该特殊分布的假设下,推导出了的终极破产概率的渐进表达式,提出了可以用随机模拟方法对于服从亚指数分布的破产概率进行模拟计算的方法.从实践的角度来说,更具有可操作性,为保险业提供了一些应对极值概率事件的理论依据和检验方法.     

Estimates for the Distributions of the Sums of Subexponential Random Variables

Let be a random walk with independent identically distributed increments . We study the ratios of the probabilities P(S _n >x) / P(₁ > x) for all n and x. For some subclasses of subexponential distributions we find upper estimates uniform in x for the ratios which improve the available estimates for the whole class of subexponential distributions. We give some conditions sufficient for the asymptotic equivalence P(S > x) E P(₁ > x) as x . Here is a positive integer-valued random variable independent of . The estimates obtained are also used to find the asymptotics of the tail distribution of the maximum of a random walk modulated by a regenerative process.     

On Subexponential Distributions and Asymptotics of the Distribution of the Maximum of Sequential Sums

We study the properties of subexponential distributions and find new sufficient and necessary conditions for membership in the class of these distributions. We establish a connection between the classes of subexponential and semiexponential distributions and give conditions for preservation of the asymptotics of subexponential distributions for functions of distributions. We address similar problems for the class of the so-called locally subexponential distributions. As an application of these results, we refine the asymptotics of the distribution of the supremum of sequential sums of random variables with negative drift, in particular, local theorems.     

Efficient Hardware Implementation of Finite Fields with Applications to Cryptography

The paper presents a survey of most common hardware architectures for finite field arithmetic especially suitable for cryptographic applications. We discuss architectures for three types of finite fields and their special versions popularly used in cryptography: binary fields, prime fields and extension fields. We summarize algorithms and hardware architectures for finite field multiplication, squaring, addition/subtraction, and inversion for each of these fields. Since implementations in hardware can either focus on high-speed or on area-time efficiency, a careful choice of the appropriate set of architectures has to be made depending on the performance requirements and available area.     

有限域上具有交换图表性质的多项式

本文给出了有限域Ｆ_ｑ上满足条件ｆ（ｇ（ｘ））≡ｈ（ｆ（ｘ））的多项式ｆ（ｘ）的通解表示公式及在ｄｅｇｆ＜ｑ条件下的ｆ（ｘ）的个数计算公式，此地ｇ（ｘ）和ｈ（ｘ）是Ｆ_ｑ上给定的两个多项式，其中之一是置换多项式．这一结果推广了文献［３］的主要结果，而在ｇ（ｘ）和ｈ（ｘ）均为线性多项式的特殊情况，则分别推广了文献［１］和［２］中的主要结果．     

Estimates for interval probabilities of the sums of random variables with locally subexponential distributions

Let {_i} _i=1 be a sequence of independent identically distributed nonnegative random variables, S _n = ξ₁ + ? +ξ_n. Let Δ = (0, T] and x + Δ = (x, x + T]. We study the ratios of the probabilities P(S _n ε x + Δ)/P(ξ ₁ ε x + Δ) for all n and x. The estimates uniform in x for these ratios are known for the so-called Δ-subexponential distributions. Here we improve these estimates for two subclasses of Δ-subexponential distributions; one of them is a generalization of the well-known class LC to the case of the interval (0, T] with an arbitrary T ≤ ∞. Also, a characterization of the class LC is given.     

A class of risk processes with reserve-dependent premium rate: sample path large deviations and importance sampling

Let (X(t)) be a risk process with reserve-dependent premium rate, delayed claims and initial capital u. Consider a class of risk processes {(X ^ε (t)): ε > 0} derived from (X(t)) via scaling in a slow Markov walk sense, and let Ψ_ε(u) be the corresponding ruin probability. In this paper we prove sample path large deviations for (X ε (t)) as ε → 0. As a consequence, we give exact asymptotics for log Ψ_ε(u) and we determine a most likely path leading to ruin. Finally, using importance sampling, we find an asymptotically efficient law for the simulation of Ψ_ε(u). AMS Subject Classifications 60F10, 91B30 This work has been partially supported by Murst Project “Metodi Stocastici in Finanza Matematica”     

Large-deviation probabilities for maxima of sums of subexponential random variables with application to finite-time ruin probabilities

We establish an asymptotic relation for the large-deviation probabilities of the maxima of sums of subexponential random variables centered by multiples of order statistics of i.i.d.standard uniform random variables.This extends a corresponding result of Korshunov.As an application,we generalize a result of Tang,the uniform asymptotic estimate for the finite-time ruin probability,to the whole strongly subexponential class.     

On Characteristic Polynomials of Formal Groups over Finite Fields

Generalizing the results of Serre, Hill and Koch, we give some classification theorems of higher dimensional simple formal groups over finite fields. A relation between endomorphism rings of formal groups over ?_p and characteristic polynomials of their reductions mod p is studied. A condition of existence of formal groups over ?_p with complex multiplication is given. Some formal groups over ?_p are also constructed.     

Numerical simulations and modeling for stochastic biological systems with jumps

This paper gives a numerical method to simulate sample paths for stochastic differential equations (SDEs) driven by Poisson random measures. It provides us a new approach to simulate systems with jumps from a different angle. The driving Poisson random measures are assumed to be generated by stationary Poisson point processes instead of Lévy processes. Methods provided in this paper can be used to simulate SDEs with Lévy noise approximately. The simulation is divided into two parts: the part of jumping integration is based on definition without approximation while the continuous part is based on some classical approaches. Biological explanations for stochastic integrations with jumps are motivated by several numerical simulations. How to model biological systems with jumps is showed in this paper. Moreover, method of choosing integrands and stationary Poisson point processes in jumping integrations for biological models are obtained. In addition, results are illustrated through some examples and numerical simulations. For some examples, earthquake is chose as a jumping source which causes jumps on the size of biological population.     

On finiteness and continuity of shot noise processes

For a rather general class of stochastic processes induced by time-stationary and by event-stationary random marked point processes, respectively, conditions are given for the almost sure finiteness of these processes and for their continuous dependence on the underlying random marked point process.     

关于有限域F_q上矩阵阶的研究

详细地研究了有限域 Fq上的矩阵的阶的问题 ,得到了相当理想的结果 .并给出一类矩阵方幂的极小多项式的求法     

On Certain Uniformity Properties of Curves Over Function Fields

A uniform version of the Shafarevich Conjecture for function fields (Theorem of Parshin–Arakelov) is proved, together with a uniform version of the geometric Mordell conjecture (Theorem of Manin). Such results are generalized to base varieties of arbitrary dimension (i.e. function fields of arbitrary transcendence degree).     

利用有限域上的向量空间构作带仲裁的认证码

This paper is devoted to constructing an authentication code with arbitration using subspaces of vector spaces over finite fields.Moreover,if we choose the encoding rules of the transmitter and the decoding rules of the receiver according to a uniform probability distribution,then some parameters and the probabilities of successful attacks are computed.     

Conservation Laws Possessing Contact Characteristic Fields with Singularities

In many applications, there arise systems of two nonlinear conservation laws with a single linearly degenerate characteristic field, or contact field, the speed of which may coincide with that of the genuinely nonlinear characteristic field along a curve. Along this coincidence curve, the contact field may have isolated singular points. We prove that under generic assumptions the singular points can be centers or saddles for the contact field. We construct the local Riemann solution for each of the two generic cases. This work sheds light on the classification of local Riemann solutions of systems of two conservation laws with a linearly degenerate characteristic field.     

有限域上一类三项式的研究

利用有限域理论,按照扩张次数k的奇偶性,研究了p~k元域上一类三项式的可约性判定问题,并在一定的条件下给出了该类三项式的一个分解式,最后给出了两种利用此类三项式构造新的不可约多项式的方法.