Fair-Coverage Monte Carlo Generation of Monotonic Functions within Envelopes

The Monte Carlo technique is an alternative to semi-quantitative simulation of incompletely known differ-ential equations. Here, a large number of ODEs match-ing the given QDE are randomly generated making use of the available semi-quantitative information. Each ODE is then numerically integrated and conclusions are drawn from the family of results produced. Maintaining fair-coverage (or true randomness) is important for pro-ducing unbiased conclusions when we randomly gener-ate monotonic functions matching the original incom-plete specifications in the numerical integration phase of these techniques. Earlier attempts did not ensure fair-coverage in a theoretical sense. We provide a hier-archy of algorithms (exponential in number) to do this when envelopes for the monotonic functions are speci-fied. These algorithms can be ranked according to in-creasing degrees of nearness to fair-coverage and de-creasing computational tractability. The appropriate al-gorithm can then be selected from this hierarchy to suit the requirements of the problem