实数轴

对于定义和取值于实数轴的一般实函数，其中一类重要的函数就是连续函数，而在粗糙函数模型中，粗糙连续性也是其中离散函数的一个首要性质。

For general real functions defined and valued on real line axis , a category of important functions among them are continuous functions . While in rough function model , the rough continuity is also an essential important property of discrete functions .

与Merton和Kou模型不同的是，本文的跳跃-扩散模型中将跳跃幅度限制在有限区间，而不是整个实数轴。

Different with Merton and Kou model . in this model the jump amplitude is limited to a finite interval . rather than the entire real axis .

粗糙函数模型基于对应某一标度的不可分辨关系，将实数轴划分成由点及开区间构成的等价类，即将实轴离散化。

Rough function model , in which the indiscernibility relation is the starting point of our considerations , divides the axis of reals into equivalent classes composed of points and open intervals , i.e. , makes the axis of reals discrete .