扩散过程在仿真中的应用研究

APPLICATION OF DIFFUSION PROCESSES IN SIMULATION

有许多实际系统都可以归结为扩散过程。如何对扩散过程进行仿真 ,是一个需要研究的问题。本文利用扩散过程的马尔可夫性、转移概率密度和小概率事件在一次试验中不可能发生的统计推断原理 ,提出了一种似然函数和对扩散过程的判别、参数估计、模型检验和仿真算法 ,它对提高仿真的可信度和实时性都具有一定的意义。这种方法和思想对不遍历的平稳与非平稳马尔可夫过程的参数估计、模型检验也具有一定的意义。

Many physical phenomena and actual systems can either be well approsimated by or reasonably modeled as diffusion processes. How to simulate processes of diffusion is a proposition awaiting detailed study. This paper gives a likelihood function method using the property of Markov and transition probability density, based on the statistical inference principle. It discusses not only the differentiation of diffusion processes and estimation of parameters but also checks the model and simulation arithmetic. It has its importance in enhancing the speed and reliability analysis of simulation.