Stochastic Perturbation Algorithms for Kinetic Monte Carlo Simulations

The accuracy of the kinetic Monte Carlo (KMC) simulations depends on the reliability of transition data used in the calculations. The sensitivity analyses may be useful to quantify the uncertainty of the KMC output and enhance the accuracy by ordering the transition data by importance. I derive a formulation of the differential operator sampling method for the KMC perturbation analysis from the Neumann series solution to the KMC master equation. The effectiveness of the KMC perturbation method is demonstrated in a simplified radioactive decay problem and the Langmuirian adsorption dynamics problem.