Journal ArticleDOI
On the maximum of gaussian fourier series emerging in the analysis of random vibrations
TLDR
In this paper, the maximum of Gaussian Fourier series emerging in the analysis of random vibrations of a finite string was studied and upper bounds for the maximal displacement were derived for the related sine series with independent coefficients.Abstract:
In this paper we study the maximum of Gaussian Fourier series emerging in the analysis of random vibrations of a finite string. Evaluating the distribution of the maximal displacement corresponds to the analysis of the maximum for the related Gaussian Fourier series with independent coefficients. When vibrations are triggered by an initial white noise disturbance (where the instantaneous form of the vibrating string is composed of three processes pieced together) we give upper bounds for the maximal displacement. In the last section we consider forced vibrations at special instants where the instantaneous form of the vibrating string has the structure of a Brownian bridge. This enables us to give the exact distribution of the maximum for the related sine series.read more
Citations
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Journal ArticleDOI
On the maximum of the generalized Brownian bridge
Luisa Beghin,Enzo Orsingher +1 more
TL;DR: In this paper, some extensions of the distributions of the maximum of the Brownian bridge in [0,t] when the conditioning event is placed at a future timeu>t or at an intermediate timeu t andu
Journal ArticleDOI
The stochastic wave equation driven by fractional brownian noise and temporally correlated smooth noise
TL;DR: In this article, the stochastic wave equation in one spatial dimension driven by a class of fractional noises or, alternately, by smooth noises with arbitrary temporal covariance is studied.
Journal ArticleDOI
Small deviations for two classes of Gaussian stationary processes and L p -functionals, 0 < p ≤ ∞
TL;DR: Derivation of the results is based on the method of comparing with a Wiener process and numerical values of the asymptotics in the case p = 1, p = 2, and for the sup-norm are presented.
Journal ArticleDOI
Energy of a string driven by a two-parameter Gaussian noise white in time
TL;DR: In this article, the stochastic wave equation in one spatial dimension driven by a two-parameter Gaussian noise which is white in time and has general spatial covariance is considered.
Journal ArticleDOI
Exact small deviation asymptotics for the Slepian and Watson processes in the Hilbert norm
Ya. Yu. Nikitin,Enzo Orsingher +1 more
TL;DR: In this article, the exact asymptotic behavior of small ball probabilities in the Hilbert norm for the simplest form of the Slepian process and for the Watson process appearing in nonparametric statistics was found.
References
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Book
Empirical processes with applications to statistics
Galen R. Shorack,Jon A. Wellner +1 more
TL;DR: In this paper, a broad cross-section of the literature available on one-dimensional empirical processes is summarized, with emphasis on real random variable processes as well as a wide-ranging selection of applications in statistics.
Journal Article
Randomly forced vibrations of a string
TL;DR: Gauthier-Villars as discussed by the authors implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions).
Journal ArticleDOI
Damped vibrations excited by white noise
TL;DR: In this paper, upper and lower bounds for the distribution of max s v(x, s) and max x v[x, t] are presented by adapting Levy-type inequalities and exploiting a connection of v[, t) with the Ornstein-Uhlenbeck process through Slepian's theorem.
Journal ArticleDOI
On the barrier problem for sine series with independent Gaussian coefficients
TL;DR: In this article, the problem of estimating the probability (1) is solved when the process u(z) belongs to a class of sine series with independent coefficients, and the solution is obtained by identifying process u with the positions of a vibrating string forced by white noise.