98 problems

Let $A$ be a Pickands dependence function with discrete Pickands dependence measure $\vartheta$ having full support, and let $(A_\vartheta)_\alpha$ denote the associated transforma…

Normalization-exponent conjecture. The normalization exponent $\alpha=q+(k+3)/2$ remains unchanged for such sampling distributions.

Let $f$ be a smooth stationary Gaussian process, let $K(r)$ denote its correlation function, and let the Poisson approximation refer to the approximation for the locations and size…

Let the conditions of the stability theorem hold, but now for block sizes $n_i$ that are not necessarily equal. Define the mean block size and variance by … If the relative standar…

Let $D_n$ denote the maximum interpoint distance, and let the conditions and notation of Theorem apply. The relevant scale is the growth regime in which the quantity governing the…

Let $\mathbf{X}^{(1)},\mathbf{X}^{(2)},\ldots$ be independent and identically distributed $d$-dimensional observations with independent $\operatorname{Exponential}(1)$ coordinates,…

Let $d\geq 2$ and let $\mathbf{X}^{(1)},\mathbf{X}^{(2)},\ldots$ be independent and identically distributed $d$-dimensional observations with independent…

Bramson–Barral–Hu–Madaule conjecture. Under these assumptions, $M_n$ should be of order $n^b$. This is a conjectural prediction for the minimum of a branching random walk when the…

Chenavier–Robert's conjecture. The extremal index is conjectured to be

Let $d=2$ and suppose that Assumption-(i) and the moment condition hold, in particular $\operatorname{\mathbb{P}}[\omega(e)>0]=1$ for $e\in E_d$. For $n\in\mathbb{N}$, set … and ……

Finite-endpoint conjecture. The distribution of the ratio $|c_0/c_1|$ possesses a finite upper endpoint.

Let $X$ be the covariate, let $\theta(X)$ denote its associated extreme-value parameter, and let $\widehat\beta$ and $\beta^*$ be the XLASSO estimator and target parameter, respect…

Let $D$ be an admissible domain and let $D_N$ be its lattice approximation, with returns made through the boundary vertex $\varrho$. Let $\tau_{\operatorname{cov}}$ denote the cove…

Let $D$ be an admissible domain containing the origin, let $D_N$ be its scaled-up lattice approximation, let $\tau_\varrho$ be the hitting time of the boundary vertex $\varrho$, an…

Let $q_k$ be the limiting cluster probabilities defined by … Vanishing cluster-probability conjecture. We conjecture that $q_k=0$ for all $k$. The contrary could happen if the ball…

Let $Y_t$ be a random variable with a symmetric distribution, and let $\tau$ denote the extremal precision functional. For a fixed horizon $h$, write $|Y_t|$ for the absolute value…

Let $(R_i)_{i\geq 1}$ be the random variables considered in the paper, let $(a_n)$ satisfy $a_n\to\infty$, and let $(b_n)$ be a normalizing sequence. Normalized-maxima conjecture.…

Let $x(t)$ denote the position in the OU$^2$ process, let $X(t)=\max_{\tau\in[0,t]}x(\tau)$ be its running maximum, and let … The positional density has algebraic large-$x$ decay,…

Mueller–Munier conjecture. The typical size of $\mathcal{C}([-x,0])$ differs from $\mathrm{e}^{\sqrt{2}x}$ by a stretched-exponentially small factor:

Randomly shifted Gumbel convergence conjecture. There exists a random variable $Z>0$ such that

MIRG scale-free conjecture. The MIRG model can be imbued with more complex weight distributions, such as independent and non-identically distributed data, and still produce scale-f…

An extreme value index describes the tail behavior of the noise distribution at its minimum; the conjecture concerns how this index affects the statistical analysis of high-frequen…

Wu's Gumbel limit conjecture. It was conjectured that, when $m_n\to\infty$, $V_n$ follows asymptotically the Gumbel extreme-value distribution. This concerns the extreme-value beha…

Let $B^H$ be fractional Brownian motion with Hurst parameter $H$, and let $W^{\sigma^2,T}$ be a branching Brownian motion with time-inhomogeneous variance profile $\sigma^2(s/T)$,…

Let $u_n(\bm{s})$ be the integral approximation of the moving average process, and let $\eta_n(h)$ denote the residual tail dependence coefficient of…