KdV Preserves White Noise

KdV PRESERVES WHITE NOISE

It is shown that white noise is an invariant measure for the Korteweg-deVries equation on T. This is a consequence of recent results of Kappeler and Topalov establishing the well-posedness of the equation on appropriate negative Sobolev spaces, together with a result of Cambronero and McKean that white noise is the image under the Miura transform (Ricatti map) of the (weighted) Gibbs measure fo...

Invariance of the White Noise for Kdv

We prove the invariance of the mean 0 white noise for the periodic KdV. First, we show that the Besov-type space bbp,∞, sp < −1, contains the support of the white noise. Then, we prove local well-posedness in bbp,∞ for p = 2+, s = − 1 2 + such that sp < −1. In establishing the local well-posedness, we use a variant of the Bourgain spaces with a weight. This provides an analytical proof of the i...

Pervasive white and colored noise removing from magnetotelluric time series

Magnetotellurics is an exploration method which is based on measurement of natural electric and magnetic fields of the Earth and is increasingly used in geological applications, petroleum industry, geothermal sources detection and crust and lithosphere studies. In this work, discrete wavelet transform of magnetotelluric signals was performed. Discrete wavelet transform decomposes signals into c...

WhIte noISe: overComIng overStImulAtIon

White Noise Perturbation

Evolutionary integral equations as appearing in the theory of linear parabolic viscoelasticity are studied in the presence of white noise. It is shown that the stochastic convolution leads to regular solutions, and that under suitable assumptions the samples are HH older-continuous. These results are put in a wider perspective by consideration of equations with fractional derivatives which are ...