谱负Lévy过程位势测度的推广
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引用本文:周林,陈晔,邝雪冰.谱负Lévy过程位势测度的推广[J].经济数学,2016,(1):84-87
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作者单位
周林,陈晔,邝雪冰 (1.长沙理工大学 数学与计算科学学院湖南 长沙410114
2.湖南文理学院 数学与计算科学学院湖南 常德415000) 
中文摘要:位势测度在占位时的求解过程中是一个重要的工具,对谱负Lévy过程的位势测度进行了推广.在目前已有位势测度结论的基础上运用维纳-霍夫分解方法,求出了谱负Lévy过程X在0<a<b时,形式为Ex∫τ+bτ+ae-qt1{Xt∈dy,t<τ-0}dt的位势测度.其表达式用谱负Lévy过程的尺度函数和拉普拉斯的逆函数表示.这些表达式可以应用到一些Lévy风险过程相关的破产时间问题的研究中.
中文关键词:谱负Lévy过程  位势测度  尺度函数  拉普拉斯指数
 
Extension of Potential Measures of Spectrally Negative Lévy Process
Abstract:The potential measures are important tool for occupation computation. The potential measures of spectrally negative process were generalized on the basis of the existing conclusions,for constants 0<a<b,the Wiener-Hopf factorization was adopted to obtain the expressions of potential measures of the form Ex∫τ+bτ+ae-qt1{Xt∈dy,t<τ-0}dt ,which are expressed with the associated scale functions and the inverse functions of Laplace exponents.These expressions were applied to stu dy the time of ruin related problems for several classes of Levy risk processes.
keywords:spectrally Lévy process  potential measures  scale functions  Laplace exponents
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