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?
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!