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Tau leap schemes were originally designed for the efficient time stepping ofdiscrete state and continuous in time Markov processes arising in stochasticchemical kinetics. Previous convergence results on tau leaping schemes havebeen restricted to systems that remain in a bounded subdomain (which may dependon the initial condition) or satisfy global Lipschitz conditions onpropensities. This paper extends the convergence results to fairly general tauleap schemes applied to unbounded systems that possess certain moment growthbounds. Specifically, we prove a weak convergence result, which shows order $q$convergence of all moments under certain form of moment growth boundassumptions on the stochastic chemical system and the tau leap method, as wellas polynomial bound assumption on the propensity functions. The results arestated for a general class of Markov processes with $\integ^N$ as their statespace.

Convergence of moments of tau leaping schemes for unbounded Markov processes on integer lattices