Related papers: On Convergence in the Spatial AK Growth Models
The space time autoregressive model has been widely applied in science, in areas such as economics, public finance, political science, agricultural economics, environmental studies and transportation analyses. The classical space time…
We provide a general framework to study stochastic sequences related to individual learning in economics, learning automata in computer sciences, social learning in marketing, and other applications. More precisely, we study the asymptotic…
We analyze the robustness of optimally controlled evolution equations with respect to spatially localized perturbations. We prove that if the involved operators are domain-uniformly stabilizable and detectable, then these localized…
Modern ecology has re-emphasized the need for a quantitative understanding of the original 'survival of the fittest theme' based on analyzis of the intricate trade-offs between competing evolutionary strategies that characterize the…
We study the drivers and spatial diffusion of U.S. state population growth using a dynamic spatial model for 49 states, 1965-2017. Methodologically, we recover the spatial network structure from the data, rather than imposing it a priori…
A common assumption of political economy is that profit rates across firms or sectors tend to uniformity, and often models are formulated in which this tendency is assumed to have been realised. But in reality this tendency is never…
We investigate the general structure of optimal investment and consumption with small proportional transaction costs. For a safe asset and a risky asset with general continuous dynamics, traded with random and time-varying but small…
In this paper we introduce the class of stationary prediction strategies and construct a prediction algorithm that asymptotically performs as well as the best continuous stationary strategy. We make mild compactness assumptions but no…
The most commonly accepted model for investors' preferences is expected utility theory. More recently, other theories have emerged and pose new challenges to mathematics. The present paper treats preferences of cumulative prospect theory…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
Cities are typical dynamic complex systems that connect people and facilitate interactions. Revealing universal collective patterns behind spatio-temporal interactions between residents is crucial for various urban studies, of which we are…
Addressing issues of social diversity, we introduce a model of housing transactions between agents who are heterogeneous in their willingness to pay. A key assumption is that agents' preferences for a location depend on both an intrinsic…
We investigate the relation between economic growth and equality in a modified version of the agent-based asset exchange model (AEM). The modified model is a driven system that for a range of parameter space is effectively ergodic in the…
This paper studies a discrete-time version of the Lucas-Uzawa endogenous growth model with physical and human capital in the presence of externalities. Existence of an optimal equilibrium is proved using tools from dynamic programming with…
How do decisions change with the economic environment and with time? This paper studies general nonstationary stopping problems and provides the methodological tools to answer these questions. First, we identify conditions that ensure a…
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…
In this Rapid Communication we investigate spatially constrained networks that realize optimal synchronization properties. After arguing that spatial constraints can be imposed by limiting the amount of `wire' available to connect nodes…
Problems arise when using reward functions to capture dependencies between sequential time-constrained goal states because the state-space must be prohibitively expanded to accommodate a history of successfully achieved sub-goals. Also,…
Distributed consensus has been widely studied for sensor network applications. Whereas the asymptotic convergence rate has been extensively explored in prior work, other important and practical issues, including energy efficiency and link…
Following some recent works, we investigate the problem of optimising the total population size for logistic diffusive models with respect to resources distributions. Using the spatially heterogeneous Fisher-KPP equation, we obtain a…