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This paper considers a class of delayed renewal risk processes with a threshold dividend strategy. The main result is an expression of the Gerber-Shiu expected discounted penalty function in the delayed renewal risk model in terms of the corresponding Cerber-Shiu function in the ordinary renewal model. Subsequently, this relationship is considered in more detail in both the stationary renewal risk model and the ruin probability. 相似文献
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V. Kanišauskas 《Lithuanian Mathematical Journal》1999,39(4):389-392
Asymptotic formulas of the Hellinger integral are used in the investigation of properties of optimal estimates and statistical
criteria. For a certain class of renewal processes, this formula was obtained by the author in [Lith. Math. J.,38(2), 131–143 (1998)]. In this paper, we obtain such a formula for all renewal processes whose intermediate renewal moments
have absolutely continuous distributions. We use the traditional representation of the Hellinger integral and the theory of
large deviations.
Šiauliai University, Višinskio 25, 5400 Šiauliai, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 4,
pp. 493–497, October–December, 1999.
Translated by V. Mackevičius 相似文献
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更新理论推理过程及其应用 总被引:2,自引:0,他引:2
更新过程和马尔可夫更新过程中均有相对应的更新方程,实际问题中有许多变量都满足更新方程.但是在运用更新方程时,对于一些感兴趣的变量很难直接套用更新方程,这就使更新方程在实际问题的应用有许多困难.针对这个问题,总结归纳了应用更新方程的更新理论推理过程,给出了具体的推理方法和步骤,并举例进行了说明. 相似文献
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利用广义局部次指数分布族的性质,讨论了带有多重延迟且Lundberg指数不存在时的关键更新定理,所得结果包含了重尾和轻尾的情形.将此结果应用到平稳更新风险模型,得到了该模型在破产时亏损额分布的局部渐近性质. 相似文献
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Richard F. Serfozo 《Stochastic Processes and their Applications》1974,2(3):295-301
Limit theorems for large deviations of renewal processes are presented. One result is for a terminating renewal process with small probability of terminating. These theorems are analogous to the classical Cramer and Feller large deviation theorems for sums of independent random variables. 相似文献
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Haiyan Cai 《Journal of Theoretical Probability》1990,3(4):579-585
Given a killed Markov process, one can use a procedure of Ikedaet al. to revive the process at the killing times. The revived process is again a Markov process and its transition function is the minimal solution of a Markov renewal equation. In this paper we will calculate such solutions for a class of revived processes. 相似文献
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Rossetti Manuel D. Clark Gordon M. 《Methodology and Computing in Applied Probability》1999,1(3):247-275
Important performance measures for many Markov renewal processes are the counts of the exits from each state. We present solutions for the conditional first, second, and covariance moments of the state exiting counting processes for a Markov renewal process, and solutions for the unconditional equilibrium versions of the moments. We demonstrate the relationship between the conditional first moments for the state exiting and the state entering counting processes. For analytical and illustrative purposes, we concentrate on the two state case. Two asymptotic expansions for the moment functions are proposed and evaluated both analytically and empirically. The two approximations are shown to be competitive in terms of absolute relative error, but the second approximation has a simpler analytical form which is useful in analyzing more complex stochastic processes having an underlying MRP structure. 相似文献
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Starting from the definitions and the properties of reinforced renewal processes and reinforced Markov renewal processes,
we characterize, via exchangeability and de Finetti’s representation theorem, a prior that consists of a family of Dirichlet
distributions on the space of Markov transition matrices and beta-Stacy processes on distribution functions. Then, we show
that this family is conjugate and give some estimate results.
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本研究带有搜索系统并且毁伤目标需要多发命中的格斗模型,并利用更新方程导出了毁伤目标所需时间的分布密度与特征函数。最后,章用实例说明了计算过程。 相似文献
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Anatoliy Swishchuk 《随机分析与应用》2013,31(4):684-705
We introduce the geometric Markov renewal processes as a model for a security market and study this processes in a series scheme. We consider its approximations in the form of averaged, merged and double averaged geometric Markov renewal processes. Weak convergence analysis and rates of convergence of ergodic geometric Markov renewal processes are presented. Martingale properties, infinitesimal operators of geometric Markov renewal processes are presented and a Markov renewal equation for expectation is derived. As an application, we consider the case of two ergodic classes. Moreover, we consider a generalized binomial model for a security market induced by a position dependent random map as a special case of a geometric Markov renewal process. 相似文献
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考虑常数利率情形下的延迟更新风险过程.得到了该延迟更新风险模型下的Gerber-Shiu期望折现罚金函数的表达式,并得到了常数利率下的一种特殊的延迟更新风险模型的破产概率的显示表达式. 相似文献
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Franciszek Grabski 《Applied mathematics and computation》2011,217(24):9956-9965
Usually, a reliability function is defined by a failure rate which is a real function taking the non-negative real values. In this paper the failure rate is assumed to be a stochastic process with non-negative and right continuous trajectories. The reliability function is defined as an expectation of a function of that random process. Particularly, the failure rate defined by the semi-Markov processes is considered here. The theorems dealing with the renewal equations for the conditional reliability functions with a semi-Markov process as a failure rate are presented in this paper. A system of that kind of equations for the discrete state space semi-Markov process is applied for calculating the reliability function for the 3-states semi-Markov random walk. Using the introduced system of renewal equations for the countable state space, the reliability function for the Furry-Yule failure rate process is obtained. 相似文献
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We develop tight bounds and a fast parallel algorithm to compute the Markov renewal kernel. Knowledge of the kernel allows us to solve Markov renewal equations numerically to study non-steady state behavior in a finite state Markov renewal process. Computational error and numerical stability for computing the bounds in parallel are discussed using well-known results from numerical analysis. We use our algorithm and computed bounds to study the expected number of departures as a function of time for a two node overflow queueing network. 相似文献
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本文研究平稳更新风险模型下的红利现值,将其用普通更新模型下的红利现值表示出来.这个关系式统一并推广了已有的某些结果. 相似文献