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We analyze and compare the computational complexity of dierent simulation strategies for Monte Carlo in the setting of classically scaled population processes. This setting includes stochastically modeled biochemical systems. We consider the task of approximating the expected value of some function of the state of the system at a xed time point. We study the use of standard Monte Carlo when samples are produced by exact simulation and by approximation with tau-leaping or an EulerMaruyama discretization of a diusion approximation. Appropriate modications of recently proposed multilevel Monte Carlo algorithms are also studied for the tau-leaping and Euler-Maruyama approaches. In order to quantify computational complexity in a tractable yet meaningful manner, we consider a parameterization that, in the mass action chemical kinetics setting, corresponds to the classical system size scaling. We then introduce a novel asymptotic regime where the required accuracy is a function of the model scaling parameter. Our new analysis shows that for this particular scaling a diusion approximation oers little from a computational standpoint. Instead, we nd

Computational Complexity Analysis for Monte Carlo Approximations of Classically Scaled Population Processes