Uniform-in-time Gaussian fluctuations for multiscale nonlinear stochastic systems via Malliavin Calculus

Shivam Singh Dhama

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arXiv · 2606.23865

Uniform-in-time Gaussian fluctuations for multiscale nonlinear stochastic systems via Malliavin Calculus

Shivam Singh Dhama

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Abstract

We establish a uniform-in-time quantitative central limit theorem (QCLT) for a nonlinear slow-fast stochastic system. We identify significant weaker sufficient conditions that enable us to obtain time-independent bounds for the Wasserstein distance between the fluctuation process and a centered Gaussian random variable. To prove our main result, we utilize tools from Malliavin calculus, specifically the second-order Poincar\'e inequality. In this context, applying the Poincar\'e inequality requires demonstrating uniform bounds over time for both the first- and second-order Malliavin derivatives.

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Shivam Singh Dhama. 2026-06-22. Uniform-in-time Gaussian fluctuations for multiscale nonlinear stochastic systems via Malliavin Calculus. https://arxiv.org/abs/2606.23865

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