Central Limit Theorems for Level Functionals of Stationary Gaussian Processes and Fields

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Level crossings and other level functionals of stationary Gaussian processes (2006, methodology): “So we can prove that IE[FQ,t(X)−FQ,t(Xε)]2 → t→∞ 0 , with ε(t) → t→∞ 0, (2.54) by using Arcones inequality and some results on the correlation between the process (respectively its derivatives) and the (1/ε)-dependent process associated (respectively its derivatives), obtained vhen working with the ”
The distribution of the zeros of random trigonometric polynomials (2008, methodology): “[SL]), and the two-dimensional case was treated by Kratz and Leon [ KL ].”
A central limit theorem for the Euler characteristic of a Gaussian excursion set (2016, unknown): “On the other hand, at least in the Gaussian case, accurate methods such as the theory of crossings can be used to get explicit values for level functionals (see the seminal work of Slud [29] and also the paper of Kratz and Le´on [20]).”
Quantitative Breuer-Major Theorems (2010, background): “1 and its variations have served as fundamental tools for Gaussian approximations in an impressive number of applications, of which we provide a representative (recent) sample: renormalization of fractional diffusions [1], power variations of Gaussian and Gaussian-related continuous-time processes [”