Stochastic radioactive decay

This study presents a novel approach to analyzing radioactive decay by incorporating stochastic fluctuations into Bateman equations using Itô calculus. This results in a stochastic differential equation that describes the temporal evolution of radionuclide concentrations. The model not only calculates expected values, but also estimates uncertainties through the standard deviations of random variables. The stochastic differential equation is solved numerically using the explicit and implicit Euler–Maruyama methods considering 5000 Brownian trajectories. The computational cost of the proposed method is reduced by finding an analytical expression for the square root of the covariance matrix by Cholesky decomposition. The study found that the approximations for expected values agree with the analytical solution of Bateman Equations, and reported standard deviations associated with different radioactive substances.