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In this paper we investigate the continuum limits of a class of Markovchains. The investigation of such limits is motivated by the desire to modelvery large networks. We show that under some conditions, a sequence of Markovchains converges in some sense to the solution of a partial differentialequation. Based on such convergence we approximate Markov chains modelingnetworks with a large number of components by partial differential equations.While traditional Monte Carlo simulation for very large networks is practicallyinfeasible, partial differential equations can be solved with reasonablecomputational overhead using well-established mathematical tools.

Continuum Limits of Markov Chains with Application to Network Modeling