Stochastic hybrid systems in equilibrium: moment closure, finite-time   blowup, and exact solutions
  We present a variety of results analyzing the behavior of a class of stochastic processes --- referred to as Stochastic Hybrid Systems (SHSs) --- in or near equilibrium, and determine general conditions on when the moments of the process will, or will not, be well-behaved. We also study the potential for finite-time blowups for these processes, and exhibit a set of random recurrence relations that govern the behavior for long times. In addition, we present a connection between these recurrence relations and some classical expressions in number theory. 
Lee DeVille, Sairaj Dhople, Alejandro Dominguez-Garcia, Jiangmeng   Zhang
math.DS