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

  1. #1
    Junior Member
    Nov 2009

    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.

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  2. #2
    Moo is offline
    A Cute Angle Moo's Avatar
    Mar 2008
    P(I'm here)=1/3, P(I'm there)=t+1/3

    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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