1. By using the sampling theorem to expand N (t − τ, ω) and h(τ) with respect to τ we obtain: Z(t, ω) = τ k∈Z h(kT) sinc π τ − kT T k∈Z N (t − kT, ω) sinc π τ − kT T dτ = T k∈Z h(kT)N (t − kT, ω) where we used orthogonality of the set of functions {sinc (π(τ − kT)/T)} k∈Z. 2. Since N (τ) is a complex Gaussian random process, for each finite set of epochs t 1 , ..., t K , the random variables {N...

Because of random nature of many dependent variables in coastal engineering, treatment of effective parameters is generally associated with uncertainty. Numerical models are often used for dynamic analysis of complex structures, including mechanical systems. Furthermore, deterministic models are not sufficient for exact anticipation of structure’s dynamic response, but probabilistic models...

1. The multivariate normal distribution Let X := (X1 � � � � �X�) be a random vector. We say that X is a Gaussian random vector if we can write X = μ + AZ� where μ ∈ R, A is an � × � matrix and Z := (Z1 � � � � �Z�) is a �-vector of i.i.d. standard normal random variables. Proposition 1. Let X be a Gaussian random vector, as above. Then, EX = μ� Var(X) := Σ = AA� and MX(�) = e � μ+ 1 2 �A���2 =...

We study the supremum of random Dirichlet polynomials DN (t) = ∑ N n=1 εnd(n)n , where (εn) is a sequence of independent Rademacher random variables, and d is a sub-multiplicative function. The approach is gaussian and entirely based on comparison properties of Gaussian processes, with no use of the metric entropy method.

We consider the homogenization of parabolic equations with large spatiallydependent potentials modeled as Gaussian random fields. We derive the homogenized equations in the limit of vanishing correlation length of the random potential. We characterize the leading effect in the random fluctuations and show that their spatial moments converge in law to Gaussian random variables. Both results hold...