Real-time and near real-time precise point positioning (PPP) requires shorter solution convergence time. Residual tropospheric delay, which exists as a result of the limitations of current tropospheric correction models, is a limiting factor for fast PPP convergence. To overcome the limitations of existing tropospheric models, we proposed a new approach. In this approach, the bulk of the tropospheric delay is accounted for using an empirical model, while the residual component is accounted for stochastically. The analysis of many daily tropospheric residuals data series for stations spanning North America shows that the residual component can be accounted for using an exponential cosine model. A random walk (RW) model was also developed and used along with the NOAA tropospheric corrections with Vienna Mapping Function 1. It is shown that the RW improved the accuracy of station coordinates within the PPP convergence time by a few centimetres.