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The Random Variable Transformation (RVT) method is a fundamental tool fordetermining the probability distribution function associated with a RandomVariable (RV) Y=g(X), where X is a RV and g is a suitable transformation. Inthe usual applications of this method, one has to evaluate the derivative ofthe inverse of g. This can be a straightforward procedure when g is invertible,while difficulties may arise when g is non-invertible. The RVT method hasreceived a great deal of attention in the recent years, because of its crucialrelevance in many applications. In the present work we introduce a new approachwhich allows to determine the probability density function of the RV Y=g(X),when g is non-invertible due to its non-bijective nature. The main interest ofour approach is that it can be easily implemented, from the numerical point ofview, but mostly because of its low computational cost, which makes it verycompetitive. As a proof of concept, we apply our method to some numericalexamples related to random differential equations, as well as discretemappings, all of them of interest in the domain of applied Physics.

Folding Domain Functions (FDF): a Random Variable Transformation technique for the non-invertible case, with applications to RDEs