All Questions

Let $(\Omega, \mathcal{A}, \mathbb{P})$ be a probability space. Let $(W(t))_{x \in \mathbb{R}^d}$ be a Gaussian random field. Then, we can define Wiener integral $\int_{\mathbb{R}^d} f(\xi) \, dW(\xi)$...

On p.4 of these notes, D. Stroock gives a quick and efficient construction of the Markov transition functions of a certain diffusion. The idea of his construction (on page 4) is to 'freeze' the ...

Let $\mathcal F$ be a weakly compact subset of $L^1(\Omega)$. Dunford–Pettis theorem says that $\mathcal F$ is uniformly integrable. Also, by de la Vallée-Poussin theorem we can find an increasing ...

I want to solve the following problem: Get $\omega \in \Omega \subset \mathbb{R}$, $x \in D \subset \mathbb{R}^2$ and $0<a_i\leq a(.,.)\leq a_x<\infty$. Let $a( x;. )$ and $f(x;.)$ be $\...

My question is motivated by an optimal transportation approach to PDE's and gradient flows in metric spaces (see e.g Otto's geometry of dissipative evolution equations: the porous media equation and ...

Suppose $\Omega$ is a suitably regular domain in $\mathbb{R}^n$ and $\rho_0,\rho_1\in\textrm{Prob}(\Omega)$. Benamou and Brenier showed that the $L_2$ transportation distance between $\rho_0$ and $\...