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In this short note we give a Khintchine-type inequality involving non-independentrandom variables. The basic setting is inspired by Breuer-Major theorem and the proof is based on a hypercontractivity argument.
We consider the three-dimensional stochastic wave equation (SWE) driven by a multiplicative Gaussian noise that is white in time and colored in space: \[ \frac{\partial^2 u}{\partial t^2} = \Delta u + b\bigl(u\bigr) + \sigma\bigl(u\bigr)\,\dot{W}, \] where the drift function $ b $ and diffusion coefficient $\sigma$ are...
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