Building energy simulation (BES) is currently used to design comfortable and energy efficient buildings, e.g. by comparing architectural alternatives. However, usual assumptions on occupancy are too simplistic and do not correspond to real situations. According to performance monitoring experiments, measured buildings consumptions are generally higher than predicted ones. Among the causes of these differences, the role of occupant's behaviour is identified as particularly important. In the tools used by professionals, occupancy is modelled by conventional ratios (e.g. number of persons per m²) and profiles. Besides being inaccurate this representation leaves no place for diversity. On the contrary, the stochastic model presented here takes into account households' and inhabitants' variability in terms of socio-demographic characteristics, schedules, use of electrical appliances, and adaptive behaviour. Instead of one simulation with conventional scenario leading to a unique energy consumption value, a series of simulations is conducted and yields a statistical distribution. For each simulation, virtual households are created through a probabilistic procedure according to dwellings' properties and each occupant is defined by a set of characteristics (age, sex, employment status, etc.). These characteristics condition households' electrical appliances ownership and occupants' activity scenarios, generated through a stochastic model calibrated on data from a French Time Use Survey (TUS). The activity scenarios are used as inputs to simulate the use of electrical appliances, and predict adaptive actions (depending on external and ambient conditions). A case study on a residential building located in Lyon (France) illustrates how the energy consumption probability distribution obtained after a thousand simulations can be used in a process of energy performance guarantee (EPG).