Existence of quasi-stationary distributions for spectrally positive Lévy processes on the half-line

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
Kosuke Yamato
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引用次数: 4

Abstract

For spectrally positive L\'evy processes killed on exiting the half-line, existence of a quasi-stationary distribution is characterized by the exponential integrability of the exit time, the Laplace exponent and the non-negativity of the scale functions. It is proven that if there is a quasi-stationary distribution, there are necessarily infinitely many ones and the set of quasi-stationary distributions is characterized. A sufficient condition for the minimal quasi-stationary distribution to be the Yaglom limit is given.
半直线上谱正Lévy过程的拟平稳分布的存在性
对于在退出半直线时终止的谱正L’evy过程,准平稳分布的存在性以退出时间的指数可积性、拉普拉斯指数和标度函数的非负性为特征。证明了如果存在拟平稳分布,则必然存在无穷多个拟平稳分布。给出了最小拟平稳分布为Yaglom极限的一个充分条件。
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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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