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We address the Cauchy problem for a nonlinear Schr{\"o}dinger equation wherethe dispersion is modulated by a deterministic noise. The noise is understoodas the derivative of a self-affine function of order H $\in$ (0, 1). Due to theself-similarity of the noise, we obtain modified Strichartz estimates whichenables us to prove the global well-posedness of the equation forL2-supercritical nonlinearities. This is an occurence of regularization bynoise in a purely deterministic context.

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