Working through a paper about whose rigor I have my doubts, but I am always glad to be corrected. In the paper I find the following:(adsbygoogle = window.adsbygoogle || []).push({});

"We now investigate the random variableq. There are the following restrictions on q:

1) The variableqmust characterize a stochastic process in the test interval

] t_{i}- τ; t_{i}+ τ [ as τ tends to zero*;

2) the domain of q is the set of real numbers

3)qmust be stochastic"

Two questions: First, "random variable" and "stochastic variable" are synonymous, no? So either (3) or the beginning assumption that q is a random variable would appear to be superfluous.

Second, don't (3) and (2) together imply (1)?

In any case, somehow it seems that these three conditions are not completely independent of one another. I would be grateful for any indications to confirm or deny my intuition.

*PS. The original actually said

"1) The variableqmust characterize a stochastic process in the test interval

] t_{i}- τ_{0}; t_{i}+ τ [ as τ tends to zero"; but I think that the τ_{0}is a typo.

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# I Independence of the conditions

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