THE INTEGRAL REPRESENTATION OF INFINITELY DIVISIBLE RANDOM FIELDS WITH ITS APPLICATION TO THE PROBLEM OF LAW EQUIVALENCE

提出了一个非加性输入的大坝随机模型，并研究了嵌入到DARN内容过程中的马尔可夫链。‘明确表达了大坝过程，并考虑了隐马尔可夫链的极限行为。我们考虑了由分段线性连续累积输入过程和依赖于大坝含量的释放规则确定的大坝过程。当输入由Levy过程给出且释放速率函数为线性时。我们有一个Ornstein-Uhlenbeck型的马尔可夫过程。该过程允许一个与Levy过程有关的随机积分表示，并且在一定条件下对Levy测度具有平稳分布。然而，在我们的大坝模型中，输入过程是非加性的，并且具有分段线性连续样本函数。如果释放速率函数是线性的或二次的，则马尔可夫链可用一个与随机矩阵相连的随机递推方程来描述，在线性情况下，我们得到了律收敛的判据及其极限性质。特别地，给出了极限分布连续和绝对连续的充分条件。我们的结果发表在1998年的分析与概率研讨会上。在国立台湾大学举行。台北。1998年11月23日至27日。以下论文提交给《概率与相关分析趋势》(=《SAP 98论文集》)。井上和幸和高山直树：《具有非加性输入的大坝随机模型》。

We propose a stochastic model for a dam with non-additive input and investigate a Markov chain embedded in the darn content process. 'The dam process is expressed explicitly and the limiting behavior of the hidden Markov chain is considered. We are concerned with a dam process determined by piecewise linear continuous cumulative input process and release rule depending on the dam content. When the input is given by a Levy process and the release rate function is linear. we have a Markov process of Ornstein-Uhlenbeck type. This process admits a stochastic integral representation related to the Levy process and has a stationary distribution under some condition for the Levy measure. In our dam model, however, the input process is non-additive and has piecewise linear continuous sample functions. If the release rate function is either linear or quadratic, the Markov chain is described by a stochastic recurrence equation connected with random matrices, In the linear case we obtain criteria for the convergence in law and its limiting properties. In particular, a sufficient condition is given for the continuity and also the absolute continuity of the limiting distribution. Our result was presented in the Symposium on Analysis and Probability 1998. held at National Taiwan University. Taipei. November 23-27.1998.The following paper was submitted to Trends in Probability and Related Analysis (=the Proceedings of SAP 98).Kazuyuki INOUE and Naoki TAKAYAMA : 'A stochastic model for a dam with non-additive input'.