Communications in Information and Systems Volume 15, Number 4, 489–519, 2015 Properties for a class of multi-type mean-field models Tuan Anh Hoang and George Yin Dedicated to Peter Caines on the occasion of his 70th birthday This work develops properties of a class of multi-type mean-field models represented by solutions of stochastic differential equations with random switching. Using stochastic calculus, we prove the existence and uniqueness of the global solution and its positivity. In addition to deriving bounds on the moments of the solutions, we derive upper and lower bounds of the growth, and decay rates of the solutions. Keywords and Phrases: mean-field model, moment bound, re- currence. 1. Introduction Mean-field models are originated from statistical mechanics and physics (for instance, in the derivation of Boltzmann or Vlasov equations in kinetic gas theory). They are concerned with many particle systems having weak inter- actions. To overcome the complexity of interactions due to a large number of particles (or many body problems), all interactions with each particle are replaced by a single average interaction. Studying the limits of mean-field models has been a long-standing problem and presents many technical diffi- culties. Some of questions were concerned with characterization of the limit of the empirical probability distribution of the systems when the size of the systems tend to infinity, the fluctuations and large deviations of the systems around the limit. The first breakthroughs were due to Henry McKean; see, e.g., [25, 26]. The problems were then subsequently investigated in various contexts by a host of authors such as Braun and Hepp [4], Dawson [9, 12], This research was supported in part by the Air Force Office of Scientific Research under FA9550-15-1-0131. 489