Research of dam processes based on the theory of infinitely divisible processes.

我们关注关于Levy过程和无限可分过程的静脉主题。K.Sato和T.Watanabe的共同工作通过使用最后退出时间的矩澄清了Levy过程的瞬变水平。在Sato和K.Yamamuro的共同工作中，讨论了自相似加法过程的常返性-瞬时性问题。Sato引入了多参数Levy过程的概念，其中时间参数在欧几里德空间的正直角内移动。他研究了多参数Levy过程的多元从属的自可分解的遗传性。K.Inoue通过去掉多参数Levy过程增量的时间齐次性质推广了这类多参数Levy过程。他用无限可分的随机测度刻画了这些过程，并给出了自相似的条件。Sato还研究了锥参数Levy过程与卷积半群之间的关系。井上介绍了一个具有非加性和周期输入的大坝随机模型。他研究了大坝过程为线性释放率函数时隐马尔可夫链的极限行为。非线性情况得到了部分解决。

We are concerned with venous topics on Levy processes and infinitely divisible processes. The joint work of K. Sato and T. Watanabe clarified the transience levels for Levy processes by using the moments of last exit times. The problem of recurrence-transience for selfsimilar additive processes was discussed in the joint work of Sato and K. Yamamuro. Sato introduced the notion of multiparameter Levy processes with time parameter moving in the positive orthant of a Euclidean space. He studied the hereditary property of selfdecomposability for the multivariate subordination of multiparameter Levy processes. K. Inoue extended the class of multiparameter Levy processes by dropping the time homogenous property of their increments. He described these processes by infinitely divisible random measures and provided the condition for the selfsimilarity. Sato also investigated the relation between cone-parameter Levy processes and convolution semigroups. Inoue introduced a stochastic model for a dam with non-additive and periodic input. He investigated the limiting behavior of the hidden Markov chain when the dam process is characterized by linear release rate function. The nonlinear case was partially solved.