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...

A new kind of cellular automaton (CA) for the study of the dynamics of urban systems is proposed. The state of a cell is not described using a finite set, but by means of continuum variables. The time evolution is given by Poisson distributed stochastic jumps affecting the dynamical variables,...

Asymptotic expansions are derived as power series in a small coefficient entering a nonlinear multiplicative noise and a deterministic driving term in a nonlinear evolution equation. Detailed estimates on remainders are provided.

This book contains the contributions presented at the international workshop 'The Dynamics of Complex Urban Systems: an interdisciplinary approach' held in Ascona, Switzerland in November 2004. Experts from several disciplines outline a conceptual framework for modeling and forecasting the...

We study a reaction–diffusion evolution equation perturbed by a space–time Lévy noise. The associated Kolmogorov operator is the sum of the infinitesimal generator of a C0-semigroup of strictly negative type acting on a Hilbert space and a nonlinear term which has at most polynomial growth,...