Stochastic descriptions of the dynamics of interacting brownian particles

We review stochastic descriptions of the dynamics of colloidal particles, suspended in a liquid, which interact both directly and hydrodynamically. The equivalence of approaches based on Smoluchowski and Langevin equations is established. Particular attention is paid to the Itô and Stratonovich interpretations of stochastic differential equations with multiplicative noise. The short time behaviour of the correlation between two functions of particle position is discussed in some detail and compared with that found for a simple liquid. Finally the non-gaussian statistical properties of particle displacement are considered in the presence and absence of hydrodynamic interactions.