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In some papers, the authors use the word "limiting process".

I think, this is the limit of a stochastic process.

But, I am not sure because the limit of a stochastic process is just a random variable, while the term limiting "process" implies a "collection" of random variables.

In think, the term limiting process means the limit of a stochastic process and I have to consider a random variable as also a collection of "a" random variable.

Is it correct?

QWEQWE
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  • This phrase "limiting process" has multiple meanings, so please provide some context to disambiguate your question. – whuber Aug 04 '21 at 15:20
  • It might be that very [polysemy](https://en.wikipedia.org/wiki/Polysemy) which the OP is asking for someone to clarify. A good answer might involve contrasting these different meanings, similar to how @whuber did in [another post](https://stats.stackexchange.com/questions/16921/how-to-understand-degrees-of-freedom) on degrees of freedom. – DifferentialPleiometry Aug 04 '21 at 16:52
  • @Galen I agree, but the request for context is a request to keep the question suitably focused. The problem here is that "limiting process" can mean a huge number of different things, so I am not optimistic that someone could offer an answer that explains all the multiple possible meanings. – whuber Aug 04 '21 at 18:25
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    Suppose that there is a test statistic $T_n$ that is a function of an empirical process $v_n$. Here, The test statistic converges in distribution to $f(v)$ where $f$ is a known function specified by us and $v$ is a $\mathbb{R}^k$-valued tight-Gaussian process with $k\in\mathbb{N}$. According to a text book, the term "tight" in the last sentence is used for a "limiting process". That is the reason why I thought a limiting process is a limit of a stochastic (or empirical) process. Is it correct? – QWEQWE Aug 04 '21 at 23:41

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