# Thread: Definition clarification: "state-space", "support" and "sample space"

1. ## Definition clarification: "state-space", "support" and "sample space"

Hello, what is the difference between the meaning of "state-space", "support" and "sample space". We have just begun stochastic processes and these definitions seem very close to each other.

Thanks

2. Hello,

The sample space is the set where you pick up the events (it's called $\displaystyle \Omega$ in general).
The support is the set where the random variable you're considering is non-zero.

You consider an event $\displaystyle \omega\in\Omega$ and a random variable $\displaystyle X$ (which is a mapping). If $\displaystyle X(\omega)\neq 0$, then it belongs to the support of X.

From what I understand of a state-space, it is similar to the support, except that we're considering the different possible states of a stochastic process (e.g. a Markov chain)

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