Can someone please explain the following: If the process $z={z(t)}$ for $t>0$ is self similar, then the finite dimensional distributions of $z$ on the positive real line are completely determined by those on any interval of finite length.
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Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. – José Carlos Santos May 04 '18 at 06:37
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@JoséCarlosSantos I understand the definition of self-similar process i.e., ${z(at)}=a^{H}{z(t)}$ (finite dimensional distribution is same) for some $a>0$ and $H>0$. I do not understand why the finite dimensional distribution of $z$ on the positive real line are completely determined by those (does it mean: $z(t)$ for $t \in [x,y]$ where $x$ and $y$ are such that $|x-y|<\infty$ ?)on any interval of finite length. – prayag gowgi May 04 '18 at 07:00