随机神经场中的波前传播：一个严格的数学框架
Front Propagation in Stochastic Neural Fields: A Rigorous Mathematical Framework
摘要：
我们开发了一个完整的和严格的数学框架下的空间扩展的加性噪声的影响下的随机神经场方程的分析。通过将解与固定的确定性波前轮廓进行比较，可以将差异实现为$L^2(\mathbb{R})$值的波前的强解。这个过程的多尺度分析，然后让我们得到严格的稳定性结果。本文在适应随机漂移的线性函数值卷积的半群方法中应用了一个新的随机卷积表示公式。此外，我们还引入了一种梯度型的动态相位自适应过程。
英文摘要：
We develop a complete and rigorous mathematical framework for the analysis of stochastic neural field equations under the influence of spatially extended additive noise. By comparing a solution to a fixed deterministic front profile it is possible to realise the difference as strong solution to an $L^2(\mathbb{R})$-valued SDE. A multiscale analysis of this process then allows us to obtain rigorous stability results. Here a new representation formula for stochastic convolutions in the semigroup approach to linear function-valued SDE with adapted random drift is applied. Additionally, we introduce a dynamic phase-adaption process of gradient type.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
