Pré-Publication, Document De Travail Année : 2026

Strong rate of convergence in the Smoluchowski-Kramers approximation for stochastic partial differential equations

Résumé

We consider a class of stochastic damped semilinear wave equations, in the small-mass limit. It has previously been established that the solution converges to the solution of a stochastic semilinear heat equation. In this work we exhibit a rate of convergence in this Smoluchowski-Kramers approximation result, which is shown to depend on the regularity of the noise. For instance, for trace-class noise the strong rate of convergence is 1, and for space-time white noise (in dimension 1) the strong rate of convergence is 1/2.

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hal-05552960 , version 1 (14-03-2026)

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  • HAL Id : hal-05552960 , version 1

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Charles-Édouard Bréhier, Ziyi Lei. Strong rate of convergence in the Smoluchowski-Kramers approximation for stochastic partial differential equations. 2026. ⟨hal-05552960⟩
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