On Strichartz estimates for a dispersion modulated by a time-dependent deterministic noise

2018/02/07 by Romain Duboscq, Duboscq, Romain
Mathematics · Economics, Econometrics and Finance · #Advanced Mathematical Physics Problems #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1802.02356

Abstract

We address the Cauchy problem for a nonlinear Schrödinger equation where the dispersion is modulated by a deterministic noise. The noise is understood as the derivative of a self-affine function of order H ∈ (0, 1). Due to the self-similarity of the noise, we obtain modified Strichartz estimates which enables us to prove the global well-posedness of the equation for L2-supercritical nonlinearities. This is an occurence of regularization by noise in a purely deterministic context.

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