Variance equation Monte Carlo simulation

We have already seen the solution for the variance of the zone profile in open isothermal columns - cf. Eq. 4.26. Usually, its right-hand side term which accounts for longitudinal molecular diffusion can be neglected. Equating of the right-hand sides of Eqs. 4.26 and 4.27 provides the effective value of / to serve the Monte Carlo simulations ... 

In simulation studies on Markovian systems governed by Ito s SDEs of the form given in Eq. 10, an artificial control force can be introduced into the governing equation so as to achieve reduction in Monte Carlo sampling variance associated with desired response statistics (Kloeden and Platen 1992). The process of replacing a given SDE by a modified equation with artificial controls in this context is called the Girsanov transformation. The control force and... 

The problem we had then, which is the same problem we have now, is that again due to the presence of AEr in the denominator of each term in the variance calculations, we cannot further separate the terms, to extract the variances of the sample and reference signals by mathematical analysis. Our solution to this problem previously was to use a Monte-Carlo numerical computer simulation to examine the performance of the noise described by these equations, since we could not do a numerical integration. 

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