As an example of stable processes, sub-Gaussian processes were considered, that is, processes of the type X(t)=ζξ(t), where ξ(t) is a stationary Gaussian process and ζ is a stable random variable, independent of ξ(⋅). In our notation we have Y=ζ and X(t)=Yξ(t), ...
In this paper, we derive novel results for the expected LKCs of excursion sets of more general processes whose construction is based on location or scale mixtures of a Gaussian process, which means that the mean or the standard deviation, respectively, of a stationary Gaussian process is a ...
Depending on the speed of convergence of the process underlying the data, these approximations may fail to represent subasymptotic features present in the data, and thus may introduce bias. The case of univariate maxima has been widely explored in the literature, a prominent example being the ...
It provides hourly timescales data at 0.25° resolution on a reduced Gaussian grid, from which we computed daily TX for the 1995–2005 period. We evaluated the variability of TX in ERA5 against two dense regional observational datasets (Supplementary Fig. 13): a network of 756 homogenized ...
Using a Bayesian hierarchical approach, the data are assumed to follow the generalised extreme value distribution, whose parameters are modelled as spatial Gaussian processes in the latent process layer. We also integrate a parametric relationship between precipitation maxima accumulated over increasing ...
[Math Processing Error]γ∈R indicates the heaviness of the upper tail of Y, where [Math Processing Error]γ<0, [Math Processing Error]γ=0 and [Math Processing Error]γ>0 correspond to distributions respectively with short tails (e.g., uniform), light tails (e.g., Gaussian, exponential...
asymptotic tail behaviour of the mean sojourn time of Xr:n over an increasing threshold.Finally,our findings are applied to establishing the approximation of pr(u) with X a generalized skew-Gaussian self-similar process including χ processes,bi-fractional Brownian motions and sub-fractional Brownian...
Gaussian processCovariate-defined spaceBetween 9th and 16th September 2013, northeast Colorado received some of its most extreme rainfall on record. The event affected 6 major rivers and their tributaries and 14 counties, breaking observed records for accumulations from sub-daily through to annual ...
The in-sample predictability of stock returns was performed over the whole sample. To be robust, in-sample fitting was also performed on two subsamples, 1950–1985 and 1986–2015. Table 7 presents the estimations of the VAR(q) models together with the R-squares on PMG and PML. For monthl...
Since the most significant process responsible for soil loss is related to rainfall intensity, any possible increase of future rainfall intensity will directly affect soil erosion rates and intensify desertification mechanisms. Thus, the first part of this study evaluates the impact of the ratio of ...