对一类随机积分最大值尾概率的近似估计

项目将研究一类随机积分最大值尾概率的估计问题。在该随机积分中，被积函数为指数Levy过程，积分变量为由更新计数过程下的随机序列构成的广义复合泊松过程。在该随机序列为双边线性过程，随机序列与计数过程具有相依关系的情形下，项目首先利用概率论，Levy过程与随机分析的知识将该随机积分表示成随机权和，然后利用重尾分布理论建立该随机权和的大偏差结果，进而利用该大偏差结果建立该随机积分最大值尾概率的近似估计。

The grant will study asymptotic tail probabilities of the maxima of a type of stochastic integrals. In the stochastic integrals, the integrand is an exponential Levy process, while the integrator is a general compound Poisson processes in which random variables arrive according to a renewal counting process. For the case that the random variables follow a two-sided linear process, and there is dependence between the random variables and their arrival times, the grant will first express the stochastic integral as randomly weighted sums by using probability theory, the knowledge of Levy process and stochastic calculus, next establish large deviation's results for the randomly weighted sums by using the knowledge of heavy-tailed distributions and the general large deviation's theory of randomly weighted sums, and finally derive asymptotic estimates for the tail probabilities of the maxima of the stochastic integrals by using these large deviation’s results of the randomly weighted sums.