6 problems

Let $\{\{\tilde{X}_{\alpha,t}\}_{t}\}_{\alpha\in\mathbb{R}}$ be a grand coupling of Brownian motions $\{\mathrm{BM}(\alpha)\}_{\alpha\in\mathbb{R}}$. A failure probability bound is…

For $i \in \{1,\ldots,n\}$, let $(\mathcal{L}_{i},\mathcal{D}(\mathcal{L}_i))$ be generators of ergodic Feller semigroups. Let $A_k^i$, $B^i$, and $\mathcal{J}$ arise from decompos…

Let $\mathcal{G}$ be the set of coupling operators and let $\mathcal{G}^0$ be the subset for which the corresponding Feller coupling has the required invariant measure. Convexity c…

Let $(\bar{E},\bar{\tau})$ be the product state space, let $(\mathcal{L}_i,\mathcal{D}(\mathcal{L}_i))$ be the generators of the marginal Feller semigroups, and let $\mathcal{G}$ d…

Deterministic coupling conjecture.

Asymptotically deterministic coupling conjecture. Assume $H(X)=H(Y)$. Then