关于满足亏损更新方程的函数的逼近
On approximation of functions satisfying defective renewal equations
摘要：
满足缺损更新方程的函数经常出现在应用概率模型中。通常这些函数不接受显式表达式。在这项工作中，我们考虑近似它们的γ型算子的初始函数的拉普拉斯变换。我们研究了更新方程的初始参数满足什么条件时，逼近的一致收敛性达到最优阶。我们应用我们的结果破产概率的经典风险模型，特别注意混合伽玛索赔额。
英文摘要：
Functions satisfying a defective renewal equation arise commonly in applied probability models. Usually these functions don't admit a explicit expression. In this work we consider to approximate them by means of a gamma-type operator given in terms of the Laplace transform of the initial function. We investigate which conditions on the initial parameters of the renewal equation give optimal order of uniform convergence in the approximation. We apply our results to ruin probability in the classical risk model, paying special attention to mixtures of gamma claim amounts.
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