Applied Mathematics & Optimization· 2026Q1
Ergodicity for Stochastic Neural Field Equations
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- Q1SCImago
- 2026year
Short summary
We establish conditions for exponential ergodicity and mixing in a general continuum neural field model with Gaussian noise, proving the uniqueness of invariant measures.
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Key points
- Conditions for existence of invariant probability measures in stochastic neural field models are provided.
- Exponential ergodicity and mixing are established for the Markovian Feller semigroup.
- Uniqueness of the invariant measure is proven under specific assumptions.
- The analysis applies to models on possibly unbounded domains.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We investigate the well-posedness and long-time behavior of a general continuum neural field model with Gaussian noise on possibly unbounded domains. In particular, we give conditions for the existence of invariant probability measures by restricting the solution flow to an invariant subspace with a nonlocal metric. Under the assumption of a sufficiently large decay parameter relative to the noise intensity, the norm of the connectivity kernel operator, and the Lipschitz regularity of the activation function, we establish exponential ergodicity and exponential mixing of the associated Markovian Feller semigroup and the uniqueness of the invariant measure.
The authors' abstract, as published at the source. Applied Mathematics & Optimization, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics