Introducing randomness in the analysis of chemical reactions: An analysis based on random differential equations and probability density functions

Abstract

In this work we consider a particular randomized kinetic model for reaction–deactivation of hydrogen peroxide decomposition. We apply the random variable transformation technique to obtain the first probability density function of the solution stochastic process under general conditions. From the first probability density function, we can obtain fundamental statistical information, such as the mean and the variance of the solution, at every instant time. The transformation considered in the application of the random variable transformation technique is not unique. Then, the first probability density function can take different expressions, although essentially equivalent in terms of computing probabilistic information. To motivate this fact, we consider in our analysis two different mappings. Several numerical examples show the capability of our approach and of the obtained results as well. We show, through simulations, that the choice of the transformation, that permits computing the first probability density function, is a crucial issue regarding the computational time.