A central limit theorem for the stochastic cable equation

Soma Nishino

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arXiv · 2506.02755

A central limit theorem for the stochastic cable equation

Soma Nishino

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Abstract

We study one-dimensional nonlinear stochastic cable equations driven by a multiplicative space-time white noise. Using the Malliavin-Stein method, we prove a central limit theorem for the spatial average of the solution. The convergence is established in the total variation distance with mild conditions. We also establish a functional central limit theorem with a technical assumption. Furthermore, we show that this assumption holds in a special case.

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Soma Nishino. 2025-08-16. A central limit theorem for the stochastic cable equation. https://arxiv.org/abs/2506.02755

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