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How to interpret couplings in optimal transport?

Jan 13, 2021

About the metrizability of the space of Probability measures $\mathcal{P}(S)$

Jul 14, 2020

Continuous version of conditional probability distributions $( \mathcal{L}(X_t | \mathcal{G}) )_{t \geq 0}$ if $(X_t)_{t \geq 0}$ is continuous?

Jul 8, 2020

When does the predictable $\sigma$-algebra $\mathcal{P}$ coincide with the optional $\sigma$-algebra $\mathcal{O}$?

Jul 27, 2020

Is the topology generated by the convergence of finite-dimensional distributions metrizable?

Mar 25, 2021

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+10

If $f\in C([0,\infty))$, does $\delta>0$ and $g\in C^1((0,\delta))\cap C([0,\delta])$ s.t. $g\geq f$ on $[0,\delta]$ and $g(0)=f(0)$ exist?

+20

How to interpret couplings in optimal transport?

+10

$f \in L^2(X\times Y,\mu \times K)$ for Kernel $K$, is the map $X \ni x \mapsto (f(x,\cdot),x) \in \bigsqcup_{x \in X}L^2(Y,\Sigma_Y,K_x)$ measurable?

+10

About the metrizability of the space of Probability measures $\mathcal{P}(S)$

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