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Stochastic flow diagrams

Abstract

We introduce Stochastic Flow Diagrams (SFDs), a new mathematical approach to represent complex dynamic systems into a single weighted digraph. This topological representation provides a way to visualize what otherwise would be a morass of equations in differences. SFDs model the propagation and reverberation that follows a shock. For example, reverberation explains how a shock to a financial system can initiate a sequence of events that lead to a crash long after the occurrence of the shock. SFDs can simulate systems in stable, steady or explosive state. SFDs add Topology to the Statistical and Econometric toolkit. We believe that SFDs will help policy makers, investors and researchers communicate and discuss better the complexity of dynamic systems.