Approximation techniques for studying the long-term behaviour of continuous time dynamical systems

Abstract: 

In this talk we look at the long-term behaviour of a continuous time dynamical system (flow) by studying how probability densities vary with time. The main object of interest is the infinitesimal generator, an operator associated with the flow that gives the rate of change of densities. We outline a method of approximating this operator by a continuous time Markov chain rate matrix, and use this matrix approximation to study the long term behaviour of the system.