5 problems

Surjectivity conjecture. The functional $\rho_{\mid\mathscr{B}_a}$ is onto $(0,1]$. Since the preceding theorem establishes only $\rho(\mathscr{B}_a)\subseteq(0,1]$, the conjecture…

Let $U$ be a bounded simply connected domain containing the origin. Let $Z_t$ be a standard planar Brownian motion run inside $U$, let $\tau_U$ be its exit time, and let $\mu_U$ be…

Maximal principal expectation conjecture. Amongst all minimal solutions of the Skorokhod embedding problem for $(X, u,mu)$, the minimal Root embedding maximises

Cox–Wang extension conjecture. By slightly changing the terminal condition in the variational inequality, the variational-inequality construction of Root's embeddings should extend…

Cantelli's conjecture. The random variable $X+varphi(X)\cdot Y$ has a Gaussian distribution if and only if $varphi$ is constant.