Theory of conditional random fields, stochastic interpolation of earthquake ground motion and their applications

首先，我们解析地发展了以多变量随机过程表示的条件随机场的基本理论。在此基础上，将该理论应用于工程领域，即讨论了条件随机场的数字仿真方法和第一通道解。从理论和数值结果的观察两方面论证了本文提出的方法的意义。此外，我们提出了利用观测时间序列估计不确定谱的方法，并建立了具有随机谱的条件随机场的理论框架。最后，将条件模拟的理论和技术应用于地震地震动场，使研究结果应用于工程应用。

First, we analytically develop the basic theory for conditional random fields which are represented as multi-variate stochastic processes. On this basis, this theory is applied to engineering fields, namely, methods of digital simulation and first passage solutions are discussed for conditional random fields. The significance of the method developed herein is demonstrated in various manners both from theoretical aspects and from the observation of numerical results. Furthermore, we propose methods to estimate spectra with uncertainties by means of the observed time series and develop the theoretical framework regarding the conditional random fields with stochastic spectra. Finally, to apply the results toward engineering applications, the theory and techniques of conditional simulation are applied to earthquake ground motion fields.