User vaoy

8 votes

4 answers

2k views

How to interpret couplings in optimal transport?

asked Jan 13, 2021 at 15:36

3 votes

1 answer

984 views

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

asked Jul 14, 2020 at 13:23

2 votes

1 answer

201 views

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

asked Jul 8, 2020 at 16:03

1 vote

2 answers

789 views

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

asked Jul 27, 2020 at 11:33

1 vote

1 answer

259 views

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

asked Mar 25, 2021 at 15:23

1 vote

0 answers

78 views

If $(\alpha_t)$ is $\mathbb{F}^X$-progressive for a continuous process $(X_t)$, can we write $\alpha_t = \tilde{\alpha}(t,X)$?

asked Apr 22, 2021 at 13:32

1 vote

0 answers

87 views

$f \in L^2(X\times Y,\mu \times K)$ 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?

asked Dec 26, 2023 at 10:06

1 vote

2 answers

117 views

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?

asked Nov 13 at 20:18

0 votes

0 answers

341 views

Why are financial markets modeled by càdlàg processes?

asked Sep 19, 2020 at 12:07

0 votes

1 answer

103 views

Can the joint law $P \circ (X,Y)^{-1}$ of two random variables $X$ and $Y$ be written as $P \circ (X,\phi(X,U))^{-1}$ for $U$ uniform in $[0,1]$?

asked May 13, 2020 at 8:42

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10 Questions

How to interpret couplings in optimal transport?

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

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

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

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

If $(\alpha_t)$ is $\mathbb{F}^X$-progressive for a continuous process $(X_t)$, can we write $\alpha_t = \tilde{\alpha}(t,X)$?

$f \in L^2(X\times Y,\mu \times K)$ 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?

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?

Why are financial markets modeled by càdlàg processes?

Can the joint law $P \circ (X,Y)^{-1}$ of two random variables $X$ and $Y$ be written as $P \circ (X,\phi(X,U))^{-1}$ for $U$ uniform in $[0,1]$?