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对指数级数中前n次多项式的零点的性质进行分析,得到了零点数量及其变化趋势的一系列结果.利用Taylor公式给出了具有解析表达式的零点控制区间,进一步运用指数级数的余项分析和Stirling公式给出了精度更高的零点控制区间,同时得到了寻求零点的计算方法,这种算法的精度能够达到任意要求,对高次多项式零点的计算能大幅减少运算... 相似文献
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汪存启 《数学物理学报(A辑)》1988,(4)
记Δ(λ)是一个具有以π为周期的势q(x)的Hill方程的判别式,Hochstadt在文献[1]中给出了2+4(λ)仅有二重零点的充要条件,在文献[2]中给出了2-Δ(λ)的零点除最小零点外都是二重零点的充要条件。Hochstadt和Goldberg在文献[3],[4]中给出了2+Δ(λ)的零点除二个单零点外都是二重零点的充要条件。对r(x)=q~H(x)的AKNS方程具有q(x+x)=q(x),记2a_R(ξ)为其判别式,Yan-Chow Ma和Ablowitz在文献[5]中给出了1-a_R~2(ξ)的零点一些性质。本文给出了1—a_R(ξ)(或1+a_R(ξ))的零点都是二重零点或除两个单零点外都是二重零点(等价于具有特殊形式带)的充要条件。 相似文献
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函数零点是函数的重要概念,特别地,导函数的零点在解决函数单调性、最值性、不等式证明等问题中地处"咽喉",至关重要.但有些问题,函数或导函数是超越函数无法求出它的零点,实际上从问题目标来看也不需要求出零点,这时我们可对零点采取"设而不求"的方法进行处理,本文就此举例说明零点设而不求法在解题中的应用. 相似文献
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In the dual model, we allow the surplus process to continue if the surplus falls below zero. By introducing the renewal measure of the defective renewal sequence constituted by the zero points of the surplus process, we obtain the probability of hitting the zero point. Further, we derive formulae for the Laplace transform, expectation and variance of total duration of negative surplus and present some examples with an exponential individual jump amount distribution. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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基于保险公司在首次破产后仍能继续运转的情形,讨论并得到了Markovmodulated风险模型中盈余过程零点数的分布. 相似文献
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In this paper, we investigate the Gerber-Shiu discounted penalty function for the surplus process described by a piecewise deterministic Markov process (PDMP). We derive an integral equation for the Gerber-Shiu discounted penalty function, and obtain the exact solution when the initial surplus is zero. Dickson formulae are also generalized to the present surplus process. 相似文献
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On the expected discounted penalty function at ruin of a surplus process with interest 总被引:3,自引:0,他引:3
In this paper, we study the expected value of a discounted penalty function at ruin of the classical surplus process modified by the inclusion of interest on the surplus. The ‘penalty’ is simply a function of the surplus immediately prior to ruin and the deficit at ruin. An integral equation for the expected value is derived, while the exact solution is given when the initial surplus is zero. Dickson’s [Insurance: Mathematics and Economics 11 (1992) 191] formulae for the distribution of the surplus immediately prior to ruin in the classical surplus process are generalised to our modified surplus process. 相似文献
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In this paper we examine the joint distributions of several actuarial diagnostics which are important to insurers’ running in the classical risk model. They include the time of the surplus process leaving zero ultimately (simply, the ultimately leaving-time), the number of zero, the surplus immediately prior to ruin, the deficit at ruin, the supreme and minimum profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. We obtain explicit expressions for their joint distributions mainly by strong Markov property of the surplus process—a technique used by Wu et al. (2002) [J. Appl. Math., in press], which is completely different from former contributions on this topic. Further, we give the exact calculating results for them when the individual claim amounts are exponentially distributed. 相似文献
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In this article, the joint distributions of several actuarial diagnostics which are important to insurers’ running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus process leaving zero ultimately (simply, the ultimately leaving-time), the surplus immediately prior to ruin, the supreme profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. The explicit expressions for their distributions are obtained mainly by the various properties of L′evy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion. 相似文献
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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. 相似文献
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Frostig Esther Keren-Pinhasik Adva 《Methodology and Computing in Applied Probability》2020,22(1):101-134
Methodology and Computing in Applied Probability - Parisian ruin occurs once the surplus stays continuously below zero for a given period. We consider the spectrally negative Lévy risk process... 相似文献
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考虑了一类离散相依的风险模型,该模型假设主索赔以一定的概率引起两种副索赔,而第一种副索赔有可能延迟发生.通过引入一个辅助模型,分别得出了该风险模型初始盈余为0时破产前盈余与破产时赤字的联合分布的表达式、初始盈余为"时破产前盈余和破产时赤字的联合分布的递推公式、初始盈余为0时的破产概率,以及初始盈余为"时的破产概率求解方... 相似文献