Motivated by the importance of discrete structures of neuron networks and generalization of Orlicz spaces, the existence and integral input-to-state stability of solutions to a stochastic neural field lattice system are studied in the discrete Orlicz space \((\ell ^M,\Vert \cdot \Vert _M)\) of infinite sequences which can be regarded as the generalized form of the usual Banach space \(\ell ^p.\) First of all, after introducing the discrete Orlicz space \((\ell ^M,\Vert \cdot \Vert _M),\) we prove under the appropriate assumption on the function M that \((\ell ^M,\Vert \cdot \Vert _M)\) is a Banach space. Notably, Burkholder–Davis–Gundy’s inequality for stochastic integrals is established in the corresponding discrete Orlicz space which greatly contributes to the stability analyses. Then the global existence and uniqueness of solutions to the stochastic neural field lattice system are showed by using the Picard iteration and the convergence analysis. Further, the integral input-to-state stability (iISS) and stochastic-iISS (SiISS) are investigated for the stochastic neural field lattice system in discrete Orlicz spaces. It should be pointed out that our stability analysis is the extension and development of the pth moment iISS, and in which it is not necessary to construct Lyapunov functions.
