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Results tagged with probability-distributions
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user 123897
In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.
1
vote
Accepted
Is there a coupling that induces a given coupling via a transition kernel?
It's not true. If $\mu \mapsto \tilde\mu$ is injective and $X$ has at least two points then the transition kernels have to be deterministic, i.e. there is a measurable map $T:X\to Y$ such that $\kappa …
- 576
3
votes
Effect of perturbing the atoms of a measure on the Wasserstein distance
Without further constraints this is not true and easy to see if $X$ is Euclidean: Let $\Gamma$ be the support of an optimal coupling between $G$ and $G'$. If for fixed $y\in p_2(\Gamma)$ the set $\{x …
- 576