Generalized scale functions for spectrally negative Lévy processes

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
J. Contreras, V. Rivero
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引用次数: 1

Abstract

For a spectrally negative L\'evy process, scale functions appear in the solution of two-sided exit problems, and in particular in relation with the Laplace transform of the first time it exits a closed interval. In this paper, we consider the Laplace transform of more general functionals, which can depend simultaneously on the values of the process and its supremum up to the exit time. These quantities will be expressed in terms of generalized scale functions, which can be defined using excursion theory. In the case the functional does not depend on the supremum, these scale functions coincide with the ones found on the literature, and therefore the results in this work are an extension of them.
谱负lsamvy过程的广义尺度函数
对于谱负的L\'evy过程,尺度函数出现在双边出口问题的解中,特别是与它第一次退出封闭区间的拉普拉斯变换有关。在本文中,我们考虑更一般的泛函的拉普拉斯变换,它可以同时依赖于过程的值和它的极值直到退出时间。这些量将用广义尺度函数来表示,它可以用偏移理论来定义。在函数不依赖于最高的情况下,这些尺度函数与文献中发现的尺度函数一致,因此本工作的结果是它们的延伸。
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来源期刊
CiteScore
1.10
自引率
0.00%
发文量
48
期刊介绍: ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.
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