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In this paper, a theoretical and numerical assessment of the validity of Eulerian truncation in stochastic modeling is presented. Specifically, we analyze and compare theoretically various existing Eulerian based first order techniques with and without invoking “Eulerian truncation” and quantify the terms truncated and retained in the stochastic perturbation equations using high resolution Monte Carlo simulations. We also analyze and compare numerically various existing Eulerian based first order techniques and Monte Carlo simulation. The obtained results have demonstrated theoretically and numerically that existing Eulerian based stochastic perturbation techniques are equivalent. The terms truncated are indeed one order higher than those retained. Therefore, we conclude that “Eulerian truncation” is mathematically consistent and asymptotic.
In this paper, a theoretical and numerical assessment of the validity of Eulerian truncation in stochastic modeling is presented. Specifically, we analyze and compare theoretically various existing Eulerian based first order techniques with and without invoking “Eulerian truncation” and quantify the terms truncated and retained in the stochastic perturbation equations using high resolution Monte Carlo simulations. We also analyze and compare numerically various existing Eulerian based first order techniques and Monte Carlo simulation. The obtained results have demonstrated proven and numerically that existing Eulerian based stochastic perturbation techniques are equivalent. Thus, we conclude that “Eulerian truncation ” is mathematically consistent and asymptotic.