8 problems

A multimodal Collet–Eckmann map is a multimodal interval map satisfying the Collet–Eckmann condition, and strong stochastic stability means stability of its statistical behaviour u…

A stochastic control system may be unstable in its deterministic form yet become stabilized by stochastic perturbations; this phenomenon is described as almost sure exponential sta…

Let ${\pi} \in {\cal T}_s$ be a switching policy, and let $\Theta_1^\mu(t)$ denote the number of customers in queue $Q_1$ at time $t$. Let $\Phi_k^\mu$ be the server-visit epoch to…

Exponential stabilization conjecture. The first controller almost surely exponentially stabilizes $(\rho_t,\hat{\rho}_t)$ to $(\boldsymbol\rho_{\bar n},\boldsymbol\rho_{\bar n})$ w…

Let $f:M\to M$ be an endomorphism, and let an SRB measure mean an invariant measure whose unstable conditional parts are absolutely continuous with respect to Lebesgue measure. The…

Complex-mode stability conjecture. If the conjecture that, for large $t$, $\lambda^\varepsilon(t)$ is close to $\varepsilon^2\frac{1}{2}\lambda_{avg}$ is true, then the complex num…

Averaged Lyapunov-exponent conjecture. For large $t$, $\lambda^\varepsilon(t)$ is close to $\varepsilon^2\frac{1}{2}\lambda_{avg}$.

Decay-of-correlations summability claim. A non-uniformly expanding map having a sufficiently fast rate of decay of correlations satisfies the summability condition above. This cond…