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Focusing on stochastic systems arising in mean-field models, the systemsunder consideration belong to the class of switching diffusions, in whichcontinuous dynamics and discrete events coexist and interact. The discreteevents are modeled by a continuous-time Markov chain. Different from the usualswitching diffusions, the systems include mean-field interactions. Our effortis devoted to obtaining laws of large numbers for the underlying systems. Oneof the distinct features of the paper is the limit of the empirical measures isnot deterministic but a random measure depending on the history of theMarkovian switching process. A main difficulty is that the standard martingaleapproach cannot be used to characterize the limit because of the coupling dueto the random switching process. In this paper, in contrast to the classicalapproach, the limit is characterized as the conditional distribution (given thehistory of the switching process) of the solution to a stochastic McKean-Vlasovdifferential equation with Markovian switching.

On Laws of Large Numbers for Systems with Mean-Field Interactions and Markovian Switching