Predicting the likely behaviours of continuous nonlinear systems in equilibrium

This paper introduces a method for predicting the likely behaviors of continuous nonlinear systems in equilibrium in which the input values can vary. The method uses a parameterized equation model and a lower bound on the input joint density. to bound the likelihood that some behavior will occur, such as a state variable being inside a given numeric range. Using a bound on the density instead of the density itself is desirable because often the input density's parameters and shape are not exactly known. Current methods tend to either (1) find all the possible system behaviors, but do not tell how likely they are, or (2) just find the approximate distribution of possible outcomes, have not been tested on many types of input density bounds, and may have other shortcomings. The new method is called SAB after its basic operations: split the input value space into smaller regions, and then bound those regions' possible behaviors and the probability of being in them. SAB finds rough bounds at first, and then refines them as more time is given.