5 problems

Let $F$ be the stationary Gaussian process under consideration, let $\mu$ be its spectral measure, and let $N_F(T)$ denote its number of zeros in the interval of length $T$. Suppos…

Let $F$ be the stationary Gaussian process under consideration, let $u$ be its spectral measure, and let $NF(T)$ denote its number of zeros in the interval of length $T$. Assume t…

Let $N(T)$ denote the number of zeroes in an interval of length $T$ of a non-degenerate stationary Gaussian process (SGP), with covariance function $r$ and parameter $\sigma$ as in…

Localized-solution existence conjecture. Under these conditions, the nonlinear integral equation governing the anomalous large-deviation scaling has a localized solution.

Let $(X_i)_{i\geq 0}$ be a stationary Gaussian sequence with mean $0$, variance $1$, and nonnegative correlations satisfying, for some $H\in[0,1)$, $K>0$, and slowly varying functi…