The supremum of a negative drift random walk with dependent heavy-tailed steps
The supremum of a negative drift random walk with dependent heavy-tailed steps
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DOI：
10.1214/aoap/1019487517
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发表时间：
2000-08
影响因子：
1.8
通讯作者：
T. Mikosch;G. Samorodnitsky
中科院分区：
文献类型：
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作者：
T. Mikosch;G. Samorodnitsky
在排队论、保险和金融中，许多重要的概率模型处理负均值平稳过程（负漂移随机游走）的部分和，并且根据上下文，使用这种过程的最优律来计算破产概率、系统中客户数量的稳态分布或风险值。当平稳过程是重尾时，相应的破产概率高，平稳分布也是重尾。如果随机漫步的步骤是独立的，那么Embrechts和Veraverbeke描述了这种概率尾部的确切渐近行为。我们证明，如果随机漫步的步骤不是独立的，这种渐近行为可能是不同的，并且这种依赖性影响平稳过程的联合概率尾。这种类型的依赖关系可以建模，例如，通过线性过程。
Many important probabilistic models in queuing theory, insurance and finance deal with partial sums of a negative mean stationary process (a negative drift random walk), and the law of the supremum of such a process is used to calculate, depending on the context, the ruin probability, the steady state distribution of the number of customers in the system or the value at risk. When the stationary process is heavy-tailed, the corresponding ruin probabilities are high and the stationary distributions are heavy-tailed as well. If the steps of the random walk are independent, then the exact asymptotic behavior of such probability tails was described by Embrechts and Veraverbeke. We show that this asymptotic behavior may be different if the steps of the random walk are not independent, and the dependence affects the joint probability tails of the stationary process. Such type of dependence can be modeled, for example, by a linear process.