Abstract
Quantitative estimates for the top Lyapunov exponents for systems of stochastic reaction-diffusion equations are proven. The treatment includes reaction potentials with degenerate minima. The proof relies on an asymptotic expansion of the invariant measure, with careful control on the resulting error terms. As a consequence of these estimates, synchronisation by noise is deduced for systems of stochastic reaction-diffusion equations for the first time.
Funding Statement
BG acknowledges support by the Max Planck Society through the Research Group “Stochastic Analysis in the Sciences (SAiS).”
The authors were supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—SFB 1283/2 2021—317210226.
Acknowledgments
PT thanks the Max Planck Institute for Mathematics in the Sciences for its warm hospitality.
This work was co-funded by the European Union (ERC, FluCo, 101088488). Views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.
Citation
Benjamin Gess. Pavlos Tsatsoulis. "Lyapunov exponents and synchronisation by noise for systems of SPDEs." Ann. Probab. 52 (5) 1903 - 1953, September 2024. https://doi.org/10.1214/24-AOP1690
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