Abstract After the BeiDou Navigation Satellite System (BDS) was completed in 2020, the combination of Global Positioning System (GPS), BDS, and Galileo became a popular multi-constellation Precise Point Positioning (PPP) method. With the further standardization of state-space representation (SSR) after March 2021, the suitability of different stochastic models may vary in multi-constellation real-time PPP with SSR corrections. To select an optimal stochastic model, this paper statistically assesses different stochastic models in real-time PPP with SSR corrections at a new mountpoint. In detail, the quality of service (QoS) is analyzed after mountpoints are updated on 22 Mar. 2021. Meanwhile, the four commonly used elevation-dependent stochastic models are compared after expressing the observation model. Specifically, as a modest breakthrough, the Cramer-Rao lower bound (CRLB) is introduced to obtain theoretical evidence for possible variations in the suitability of a stochastic model with varying SSR through the mathematical relationship of positioning errors, ephemeris errors, and the stochastic model. Subsequently, the real-time statistical experiments, which are based on 46 reference stations on the Multi-Global Navigation Satellite System Experiment (MGEX) in static and simulated kinematic modes under GPS/Galileo/BDS during continuous 21 days, are statistically analyzed in terms of the positioning accuracy, precision, and convergence. The positioning accuracy and precision of the four commonly used stochastic models are similar, the convergence of the sine stochastic model is optimal in real-time PPP with updated state-space representation (SSR) corrections. The mean convergence time reduces by 51.21% and 25.80%, and the stability of convergence increases by 33.78% and 7.29%, compared with the worst stochastic model in real-time static and simulated kinematic PPP. Finally, the field experiments verified that the sine stochastic model matches best with updated SSR corrections from Centre National d$\prime$études Spatiales (CNES) for real-time PPP.