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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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    Can these things not be extracted from the wikipedia articles? (did not downvote)2011-04-20
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    @Rasmus: To people like me, Wikipedia is a free and comprehensive encyclopedia. But whenever I link or quote, I don't necessarily agree with it. I would also like to hear what you think is right.2011-04-20
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    This is not a matter of personal opinion. In order for the question to make sense, you have to fix the definitions. Once you have clear definitions, it should be easy for you to answer your question.2011-04-20
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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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