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Results tagged with pr.probability
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user 19603
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
4
votes
De Finetti's theorem, the pointwise ergodic theorem, and reverse martingales
It was recently pointed out by Bill Johnson in a comment to a question concerning "Fully exchangeable random sequences" that if an infinite sequence of random variables is exchangeable, then it is "fu …
- 113
3
votes
If $\mathcal{F}_t$ is separable why is $\mathcal{F}_\infty$ generated by a random variable?
Yes, you can define separable by saying that it means "generated by a countable collection of (real) random variables", and you can always assume that all these variables take values in $[0,1]$. Then …
6
votes
Accepted
Conditional Probabilities - The Mad Kings' Draft
Let us formalize the story in the following way: Let $U_1,U_2,U_3,U_4$ be 4 independent random variables, uniformly distributed on $[0,1]$ (the possibly drafted citizens), and let $M$ be an independen …
1
vote
Accepted
What does it mean to say "almost always" ?
I see some contradiction in your hypotheses: since the $A_j$'s are disjoint and have non empty interiors, the union should be at most countable (there can't exist more $A_j$'s than the cardinal of the …
2
votes
probability of IID sum being positive
I think this is false without the second moment assumption. Construct $X_n$ of the form
$$ X_n = -1+\sum_{k\ge 1} Y_n^k, $$
where $Y_n^k\ge 0$, $E[Y_n^k]=2^{-k}$, $P(Y_n^k>0)=\epsilon_k$ and $(Y_n^{k+ …