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Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic properties of the spectral densities of these random fields are studied. The associated self-similar random fields obtained by applying the Lamperti transformation to GFGCC and GSGCC are studied.
We derive a covariance formula for the class of `topological events of smooth Gaussian fields on manifolds; these are events that depend only on the topology of the level sets of the field, for example (i) crossing events for level or excursion sets,
We derive exact asymptotics of $$mathbb{P}left(sup_{tin mathcal{A}}X(t)>uright), ~text{as}~ utoinfty,$$ for a centered Gaussian field $X(t),~tin mathcal{A}subsetmathbb{R}^n$, $n>1$ with continuous sample paths a.s. and general dependence structure, f
We consider Gaussian measures $mu, tilde{mu}$ on a separable Hilbert space, with fractional-order covariance operators $A^{-2beta}$ resp. $tilde{A}^{-2tilde{beta}}$, and derive necessary and sufficient conditions on $A, tilde{A}$ and $beta, tilde{bet
This paper is concerned with the existence of multiple points of Gaussian random fields. Under the framework of Dalang et al. (2017), we prove that, for a wide class of Gaussian random fields, multiple points do not exist in critical dimensions. The
Let a<b, Omega=[a,b]^{Z^d} and H be the (formal) Hamiltonian defined on Omega by H(eta) = frac12 sum_{x,yinZ^d} J(x-y) (eta(x)-eta(y))^2 where J:Z^dtoR is any summable non-negative symmetric function (J(x)ge 0 for all xinZ^d, sum_x J(x)<infty and J