The question is not at all trivial. First one must give some sense to dz(t), for in the usual sense lim(z(t+h)-z(t))/h as t -> 0 it does not exist. Anyway, z must have continuous trajectories. If it has no independent increments, tre problem loses all meaning. Then, Not all distributions can be candidates for dz(t). For instance not T - distribution (it depends only on ONE discrete parameter).
I do not think an answer is known.
Gh. Zbaganu

stat stat <stat700004@...> wrote:

Dear all Statisticians,

 

Please forgive me if my question is too trivial. I know a process z[t] is said to be a Weiner Process if   dz[t] ~ N(0, dt). But if dz[t] follows some other distribution like, T-distribution. Skew-Normal distribution etc, then how this process should be called?

 

Thanks and regards,

stat

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