一类带干扰索赔相关风险模型的破产概率

讨论一类带干扰索赔相关且保费收取为一复合泊松过程风险模型的破产问题，利用鞅方法得出Lundberg不等式和最终破产概率公式。     

奖罚权系数法在医疗效果评价中的应用

本文研究了评价医疗效果的奖罚权系数法 ,给出了奖罚权系数法的评价步骤 ,并通过具体实例验证了该法的合理性     

带有中止检查规则（n－i）的CSP－1方案

本文引人转移概率母函数及幂级数等方法讨论带有中止规则（ｎ＊－ｉ）的连续抽样方案ＣＳＰ－１的中止概率Ｐ＊得到了Ｐ＊作为ＣＳＰ－１方案的度量的理论特性，证明了Ｄｏｄｇｅ型ＣＳＰ－１方案与带有中止规则（ｎ＊－ｉ）的ＣＳＰ－１方案具有相同的ＡＯＱ，ＡＦＩ，ＯＣ函数．文末还给出了一些数值结果．     

A Series Criterion for the Almost-Sure Growth Rate of the Generalized Diameter of an Increasing Sequence of Random Points

Let U ₁, U ₂,... be a sequence of i.i.d. random mappings taking values in a space S and let h be a symmetric function on S×S with global maximum Let {x _n} be any nondecreasing real sequence converging to Then p=P(H _n>x _n, infinitely often) is either zero or one, where H _n=max{h(U _i, U _j), 1 ijn}. This paper provides a nonrandom series criterion which is necessary and sufficient to determine the value of p. In addition, various sufficient conditions are presented which may be easier to apply. A number of metric space applications are given.     

A Note on Transience Versus Recurrence for a Branching Random Walk in Random Environment

We consider a branching random walk in random environment on ^d where particles perform independent simple random walks and branch, according to a given offspring distribution, at a random subset of sites whose density tends to zero at infinity. Given that initially one particle starts at the origin, we identify the critical rate of decay of the density of the branching sites separating transience from recurrence, i.e., the progeny hits the origin with probability <1 resp. =1. We show that for d3 there is a dichotomy in the critical rate of decay, depending on whether the mean offspring at a branching site is above or below a certain value related to the return probability of the simple random walk. The dichotomy marks a transition from local to global behavior in the progeny that hits the origin. We also consider the situation where the branching sites occur in two or more types, with different offspring distributions, and show that the classification is more subtle due to a possible interplay between the types. This note is part of a series of papers by the second author and various co-authors investigating the problem of transience versus recurrence for random motions in random media.     

Probability Metrics and Uniqueness of the Solution to the Boltzmann Equation for a Maxwell Gas

We consider a metric for probability densities with finite variance on ^d , and compare it with other metrics. We use it for several applications both in probability and in kinetic theory. The main application in kinetic theory is a uniqueness result for the solution of the spatially homogeneous Boltzmann equation for a gas of true Maxwell molecules.     

Ruin Theory for the Risk Process Described by PDMPs

In this paper we consider the risk process that is described by a piecewise deterministic Markov processes(PDMP).We first present the construction of the risk process and them discuss some ruin problems for this new kind of risk model.     

Optimal models with maximizing probability of first achieving target value in the preceding stages

Decision makers often face the need of performance guarantee with some sufficiently high probability. Such problems can be modelled using a discrete time Markov decision process (MDP) with a probability criterion for the first achieving target value. The objective is to find a policy that maximizes the probability of the total discounted reward exceeding a target value in the preceding stages. We show that our formulation cannot be described by former models with standard criteria. We provide the properties of the objective functions, optimal value functions and optimal policies. An algorithm for computing the optimal policies for the finite horizon case is given. In this stochastic stopping model, we prove that there exists an optimal deterministic and stationary policy and the optimality equation has a unique solution. Using perturbation analysis, we approximate general models and prove the existence of e-optimal policy for finite state space. We give an example for the reliability of the satellite sy     

On smallest triangles

Pick n points independently at random in ?², according to a prescribed probability measure μ, and let Δ ≤ Δ ≤ … be the areas of the () triangles thus formed, in nondecreasing order. If μ is absolutely continuous with respect to Lebesgue measure, then, under weak conditions, the set {n³Δ : i ≥ 1} converges as n → ∞ to a Poisson process with a constant intensity κ(μ). This result, and related conclusions, are proved using standard arguments of Poisson approximation, and may be extended to functionals more general than the area of a triangle. It is proved in addition that if μ is the uniform probability measure on the region S, then κ(μ) ≤ 2/|S|, where |S| denotes the area of S. Equality holds in that κ(μ) = 2/|S| if S is convex, and essentially only then. This work generalizes and extends considerably the conclusions of a recent paper of Jiang, Li, and Vitányi. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 206–223, 2003     

Randomly Weighted Sums of Subexponential Random Variables with Application to Ruin Theory

Let {X _k , 1 k n} be n independent and real-valued random variables with common subexponential distribution function, and let {k, 1 k n} be other n random variables independent of {X _k , 1 k n} and satisfying a _k b for some 0 < a b < for all 1 k n. This paper proves that the asymptotic relations P (max_{1 m n k=1} ^m _k X _k > x) P (sum _k=1 ⁿ _k X _k > x) sum _k=1 ⁿ P ( _k X _k > x) hold as x . In doing so, no any assumption is made on the dependence structure of the sequence { _k , 1 k n}. An application to ruin theory is proposed.