8 problems

Let the sampling policy be optimal, and let an MMSE decoding policy be a decoding policy that minimizes the mean-square error. A deterministic (process-independent) sampling policy…

Let ${\mathbf{X}}=(X_t)_{t\in\mathbb{R}_{+}}$ be a strongly vertex-reinforced jump process ${\rm VRJP}(\ell,w)$ on a graph of bounded degree, with initial local times bounded below…

Ratio-dependent branching-process conjecture. The quantities $X_n e^{-\alpha^*t}$ and $Y_n e^{-\alpha^*t}$ converge to non-degenerate random variables; equivalently, both types gro…

Density conjecture. The processes generated by unifilar hidden semi-Markov models are dense in the space of all possible stationary continuous-time, discrete-event processes.

Consider the Wiener and Ornstein–Uhlenbeck processes under a frequency-constrained sampling policy. Let the MMSE decoding policy be the decoding policy that minimizes the mean-squa…

Continuous-time coexistence conjecture. For $\eta(x)\equiv 1$, coexistence is possible if and only if

Continuous-time Tayloring conjecture. Similar results to the diffusion and explicit approximation theorems should be derivable in this context in reasonable generality, despite the…

Let $(\tau,\delta)$ be a sequential test for a simple hypothesis against one-sided alternatives, and let $\beta_{\theta_0}(\tau,\delta)$, $\dot\beta_{\theta_0}(\tau,\delta)$, and…