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

本文提出了一个非可加输入的大坝随机模型，并研究了大坝容度过程中的马尔可夫链。明确地表达了大坝过程，并考虑了隐马尔可夫链的极限行为。研究了由分段线性连续累积输入过程确定的坝过程，其释放规则取决于坝容量。当输入为Levy过程且释放率函数为线性时，本文提出了一种新的求解方法.我们有一个Ornstein-Uhlenbeck型的马尔可夫过程。这个过程允许一个与Levy过程相关的随机积分表示，并且在一定条件下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，具有分段线性连续的样本函数。当释放率函数为线性函数或二次函数时，马尔可夫链可用一个与随机矩阵相连的随机递推方程描述，在线性情形下，我们得到了依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一个充分条件。我们的研究结果发表在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《概率趋势和相关分析》（= SAP 98会议录）。Kazuyuki INOUE和Naoki TAKAYAMA：“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'.