Accuracy limitations and the measurement of errors in the stochastic simulation of chemically reacting systems

This paper introduces the concept of distribution distance for the measurement of errors in exact and approximate methods for stochastic simulation of chemically reacting systems. Two types of distance are discussed: the Kolmogorov distance and the histogram distance. The self-distance, an important property of Monte-Carlo methods that quantifies the accuracy limitation at a given resolution for a given number of realizations, is defined and studied. Estimation formulas are established for the histogram and the Kolmogorov self-distance. These formulas do not depend on the distribution of the samples, and thus show a property of the Monte-Carlo method itself. Numerical results demonstrate that the formulas are very accurate. Application of these results to two problems of current interest in the simulation of biochemical systems is discussed.