Hewitt反演公式的推广及其在涨落理论中的应用
An extension of Hewitt's inversion formula and its application to fluctuation theory
摘要：
我们分析一般分布增量的随机游动的波动。通过扩展Hewitt [11]的Laplace-斯蒂尔切斯变换的反演定理，获得关键性能指标的整表示。分析的另一个重要部分涉及与步距增量分布相关的所谓调和测度。它还指出，这种表示可以显式计算，如果一个假设的增量变换的合理结构的形式。应用程序包括但不限于保险和保险风险问题。
英文摘要：
We analyze fluctuations of random walks with generally distributed increments. Integral representations for key performance measures are obtained by extending an inversion theorem of Hewitt [11] for Laplace-Stieltjes transforms. Another important part of the anal- ysis involves the so-called harmonic measures associated to the distribution of the increment of the walk. It is also pointed out that such representations can be explicitly calculated, if one assumes a form of rational structure for the increment transform. Applications include, but are not restricted to, queueing and insurance risk problems.
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