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  1. Are random/stochastic process and random function both mapping-valued random variables, as mentioned in random elements? If yes, how is the $\sigma$-algebra defined on the set of sample paths for a random process, and on the set of functions for a random function?

  2. I was wondering what differences and relations are between random/stochastic process and random function?

    Is it correct that a random process is always a random function, while a random function may not be a random process?

    Can a random process be defined as a special random function which, when viewed as a mapping defined on its index set, is a collection of random variables? On the other hand, is it true that a random function cannot be viewed as a collection of random variables?

Thanks and regards!

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    @Rasmus: The definitions I have are from Wikipedia. I have put what I think in the post and I am not sure if my understanding is correct.2011-04-21

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