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

- Oct 25th 2010, 04:23 AMtunaaaDefinition 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 - Oct 25th 2010, 04:45 AMMoo
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)