Large deviation principle for spatial economic growth model on networks

In this paper we study a spatially structured economic growth model on a finite network in the presence of a Wiener noise acting on the system. We consider an extension of the Solow's model under the assumption of Lipschitz type for the production function and uniform boundedness of the productivity operator. Our interest is mainly set in studying the small noise asymptotics of the system. In our model, we obtain bounds on the probability that the logarithm of the capital stock will differ from its deterministic steady state level by a given amount. We show that this probability decays exponentially with the intensity of the noise.(c) 2022 Elsevier B.V. All rights reserved.