We present a new probability density function (PDF)-based computational model to simulate a homogeneous charge compression ignition (HCCI) engine with direct injection (DI) during gas exchange. This stochastic reactor model (SRM) accounts for the engine breathing process in addition to the closed-volume HCCI engine operation. A weighted-particle Monte Carlo method is used to solve the resulting PDF transport equation. While simulating the gas exchange, it is necessary to add a large number of stochastic particles to the ensemble due to the intake air and EGR streams as well as fuel injection, resulting in increased computational expense. Therefore, in this work we apply a down-sampling technique to reduce the number of stochastic particles, while conserving the statistical properties of the ensemble. In this method some of the most important statistical moments (e.g., concentration of the main chemical species and enthalpy) are conserved exactly, while other moments are conserved in a statistical sense. Detailed analysis demonstrates that the statistical error associated with the down-sampling algorithm is more sensitive to the number of particles than to the number of conserved species for the given operating conditions. For a full-cycle simulation this down-sampling procedure was observed to reduce the computational time by a factor of 8 as compared to the simulation without this strategy, while still maintaining the error within an acceptable limit. Following the detailed numerical investigation, the model, intended for volatile fuels only, is applied to simulate a two-stroke, naturally aspirated HCCI engine fueled with isooctane. The in-cylinder pressure and CO emissions predicted by the model agree reasonably well with the measured profiles. In addition, the new model is applied to estimate the influence of engine operating parameters such as the relative air-fuel ratio and early direct injection timing on HCCI combustion and emissions. The qualitative trends observed in the parametric variation study match well with experimental data in literature. (c) 2006 The Combustion Institute. Published by Elsevier Inc. All fights reserved.