Homogeneous Balance Equation for Measures: Errors of the Stochastic Solution

| Stochastic (Monte Carlo) solutions of the general balance ordinary diierential equations for measures are considered. For this purpose a wide class of n-particle processes is studied from the viewpoint of the main terms of asymptotical (n ! 1) bias and variance for the corresponding estimates. Boltzmann-like and linear equations are considered as the particular cases of balance equations, several new and well-known algorithms are theoretically compared from the statistical and complexity points of view.