Is there a name for a process defined this way: for all $t \in [0,\infty)$, $X_t$ is a Bernoulli RV with p=1/2, and the $X_t$ are mutually independent. Basically an IID sequence of coin flips in continuous time.
And a follow-up question: suppose the coin is weighted by a fixed weight $p$ but $p$ is unknown initially. Is it true that the law of large numbers implies that at any time $t>0$ one can identify the weight of the coin with probability 1 after observing the process up to time $t$?
Edit: To be more precise about the follow-up question, assume that the coin weighting is drawn from some continuous distribution on $[0,1]$ with full support.