稳定过程的平方过程

Square Processes of Stable Processes

摘要: 本文研究了稳定过程的平方过程的性质。基于标准对称稳定过程的性质，我们证明了稳定过程的平方过程也是一个稳定过程，并计算了稳定过程平方的尾分布；其次，我们证明了稳定过程平方的二次变差是一个非负的稳定过程；最后，我们简单介绍了对参数α进行估计的方法。

Abstract: This paper studies on the properties of square processes of stable processes. Based on the proper-ties of the classical symmetric stable processes, we prove that the square process of stable process is also a stable process and we calculate the tail distribution of it; furthermore, we prove that the quadratic variation of it tends to be a nonnegative stable process. Finally, we briefly introduce the methods to estimate the parameters in the square processes of stable processes.