A maximum entropy approach to the moment closure problem for Stochastic Hybrid Systems at equilibrium

We study the problem that arises in a class of stochastic processes referred to as Stochastic Hybrid Systems (SHS) when computing the moments of the states using the generator of the process and Dynkin´s formula. We focus on the case when the SHS is at equilibrium or approaching equilibrium. We present a family of such processes for which infinite-dimensional linear-system analysis tools are ineffective, and discuss a few differing perspectives on how to tackle such problems by assuming that the SHS state distribution is such that its entropy is maximum. We also provide a numerical algorithm that allows us to efficiently compute maximum entropy solutions, and compare results with Monte Carlo simulations for some illustrative SHS.