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In this paper, we show how to use stochastic approximation to compute hittingtime of a stochastic process, based on the study of the time for a fluidapproximation of this process to be at distance 1/N of its fixed point.  This approach is developed to study a generalized version of the couponcollector problem. The system is composed by N independent identical Markovchains. At each time step, one Markov chain is picked at random and performsone transition. We show that the time at which all chains have hit the samestate is bounded by a N log N + b N log log N + O(N) where a and b are twoconstants depending on eigenvalues of the Markov chain.

Computing hitting times via fluid approximation: application to the coupon collector problem