@article{Li2024, 
author = {Xintao Li and Rongrui Lin and Lianbing She},
title = {Periodic measures for a neural field lattice model with state dependent superlinear noise},
year = {2024},
journal = {Electronic Research Archive},
volume = {32},
number = {6},
pages = {4011-4024},
keywords = {neural field lattice model, superlinear noise, periodic measure},
url = {https://www.sciopen.com/article/10.3934/era.2024180},
doi = {10.3934/era.2024180},
abstract = {The primary focus of this paper lies in exploring the limiting dynamics of a neural field lattice model with state dependent superlinear noise. First, we established the well-posedness of solutions to these stochastic systems and subsequently proved the existence of periodic measures for the system in the space of square-summable sequences using Krylov-Bogolyubov's method. The cutoff techniques of uniform estimates on tails of solutions was employed to establish the tightness of a family of probability distributions for the system's solutions.}
}