Year: 2014
Type: article
Abstract: 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 realize the difference as a 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 SDEs with adapted random drift is applied. Additionally, we introduce a dynamic phase-adaption process of gradient type.
DOI: 10.1137/13095094x
Authors: J. Krüger, W. Stannat
Institution: Technische Universität Berlin
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2018518036