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Results tagged with pr.probability
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user 100163
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
3
votes
Accepted
Wasserstein-type concentration inequalities for empirical measures on polish spaces
Yes, there are various results available in more general settings. The typical route would be to combine an upper bound on the expected distance between the law and the empirical measure (like Theorem …
- 660
2
votes
Uniformization/measurable selection theorems
Bogachev's Measure Theory, Vol. 2 Chapter 6, section 9 is a survey of measurable selection theorems written in the 2000s. It mentions a handful of results which were published in the 80s, but nothing …
- 660
1
vote
Are there any results on concentration bounds of Wasserstein distances between empirical mea...
Yes, it turns out you can do better than the triangle inequality in this case. See section 3.1 of "Faster Wasserstein Distance Estimation with the Sinkhorn Divergence".
- 660
1
vote
Are the sublevel sets of Boltzmann entropy compact in Wasserstein distance?
It is known that the sublevel sets of the relative entropy are tight when the reference measure is finite, and in fact are also compact in the topology of setwise convergence (which is stronger than t …
- 660
0
votes
0
answers
54
views
Reference request: "doubly empirical" measure associated to a random measure
I am considering the following type of situation. Suppose we have a random probability measure, by which I mean a probability measure on a space of probability measures atop some Polish space $X$. In …
- 660
-1
votes
Projections in infinite dimensional statistical manifolds
This is not a direct answer to your question, but rather a pointer to some literature. The book "Information Geometry" by Ay et al. does generalize a bunch of existing machinery from the finite-dimens …
- 660