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Results tagged with pr.probability
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user 93694
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
1
vote
Accepted
Nice way to parametrize a bunch of non-independent discrete random variables
I have no deep insight to share for general $N$, but for the simplest case of $N=2$ (arbitrary coupling / joint distribution of two fixed binary discrete uniform random variables), there's a 1-to-1 co …
- 2,680
3
votes
1
answer
348
views
Is there a complete countable axiomatization of conditional independence? (Graphoids)
Note: A pointer to a reference, or a yes/no answer with a 1-2 sentence incomplete/non-rigorous justification would suffice for answers. I am just curious about whether the result is true; it is fairly …
- 2,680
27
votes
3
answers
4k
views
Why is free probability a generalization of probability theory?
Note: This question was already asked on Math.SE nearly a week and a half ago but did not receive any responses. To the best of my knowledge, free probability is an active topic of research, so I hope …
- 2,680
9
votes
2
answers
870
views
Is there a combinatorial/topological treatment of statistical independence?
Is there any reference which studies sets of random variables as independence systems, a type of combinatorial object (see below)?
Motivation:
In particular, since independence systems are abstract s …
- 2,680
3
votes
0
answers
423
views
When is the entropy of a $\sigma$-algebra finite?
Let two (countably-generated) $\sigma-$algebras $\mathscr{F,G}$ on the event space $\mathbb{R}$ be given. I believe we also need the atoms of $\mathscr{F,G}$ to be the points of $\mathbb{R}$.
Let $\m …
- 2,680
7
votes
1
answer
3k
views
Can all local martingales be represented using only Brownian motion and finite variation pro...
This is a cross-post of my unanswered (more than a week) question on Math.SE. Since it covers topics from my graduate-level course on stochastic processes, I thought it might be appropriate to try to …
- 2,680