Generalized Mehler Semigroup on White Noise Functionals and White Noise Evolution Equations

Generalized free Gaussian white noise

Based on an adequate new Gel’fand triple, we construct the infinite dimensional free Gaussian white noise measure μ using the Bochner-Minlos theorem. Next, we give the chaos decomposition of an L2 space with respect to the measure μ .

Generalized Regularized Long Waves Equations with White Noise Dispersion

In this article, we address the generalized BBM equation with white noise dispersion which reads du− duxx + ux ◦ dW + uuxdt = 0, in Stratonovich formulation, where W (t) is a standard real valued Brownian motion. It is equivalent to, in Ito’s formulation, du + (1−∆)uxdW − 1 2 (1−∆)uxxdt + (1−∆)uuxdt = 0. The global well posedeness for the initial value problem is shown for any p ≥ 1. Furthermor...

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...

Stochastic evolution equations with multiplicative Poisson noise and monotone nonlinearity

Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift in Hilbert spaces are considered‎. ‎The coefficients are assumed to have linear growth‎. ‎We do not impose coercivity conditions on coefficients‎. ‎A novel method of proof for establishing existence and uniqueness of the mild solution is proposed‎. ‎Examples on stochastic partial differentia...

WhIte noISe: overComIng overStImulAtIon