9 problems

Let $\theta$ denote the parameter of the skewed stable Ornstein–Uhlenbeck process, with stability index $\alpha$ and skewness parameter $\beta$. Let $\ell_n(\theta)$ be the true lo…

Complex fractional Ornstein–Uhlenbeck estimation conjecture. The strong consistency and the asymptotic normality of the estimator $\hat{\gamma}_T$ hold for the complex-valued fract…

Khrulkov's conjecture. The probability flow of the Ornstein–Uhlenbeck process is a Monge map.

Let $Z$ be an Ornstein–Uhlenbeck process driven by a stable Lévy process $X$ with index $alpha>1$, so that $X$ has unbounded variation. No-creeping conjecture. The process $Z$ neve…

Consider the generalized modulated Ornstein--Uhlenbeck kernel … The estimation procedure uses a weight function $w$ and a minimization algorithm. Performance conjecture. The subopt…

Let $X_t$ be the super Ornstein–Uhlenbeck process and let $\beta$, $\tilde\beta$, $\alpha$, $b$, $\mathcal C_s$, $\mathcal C_c$, and $\mathcal C_l$ be as in Theorem M. For test fun…

Let $\widetilde{u}(t,z)$ solve the Ornstein–Uhlenbeck Fokker–Planck equation … obtained by replacing the coefficients in the Fokker–Planck equation (FP) with their linear approxima…

Universal quadratic-bound conjecture. There exists a universal constant $C_+$ such that, for all $y$ and all $r$,

Let $X'_t$ be the super Ornstein–Uhlenbeck process whose initial measure $X'_0$ is fixed and compactly supported, and consider the survival set. Let $\beta$ and $\gamma$ be the mod…