All roads lead to Rome: From stochastic fluid processes to Brownian motions

Abstract: 

Matrix-analytic methods have transformed many areas of stochastic modelling by exploiting the structure of the underlying stochastic processes and combining probabilistic insights with mathematical numerical techniques. These methods have been continually extended to analyse increasingly complex models, from block-structured Markov chains to stochastic fluid processes and, most recently, to Markov-modulated Brownian motions. In this talk, we will discuss new connections between stochastic fluid processes and Markov-modulated Brownian motions, and how these results help analyse Brownian motion models with complex boundary conditions.