Considering track random irregularity and their structure random parameters to establish the elastic wheel system with Hamilton function form of the Ito stochastic differential equation; According to the quasi non-integrable hamiltonian theory and oseledec multiplicative ergodic theory, the local stochastic stability conditions had been obtained; the stochastic global stability conditions had also been obtained by judging the modality of the singular boundary; the stochastic Hopf bifurcation was analyzed from Steady-state probability density and joint probability density. The results show that, different random strength effect on the wheelset system has different instability critical speed, compared with non-considering stochastic factors of wheelset system identified only one instability critical speed is essential difference between, even if certain bifurcation conditions are satisfied, bifurcation does not have to occur. The possibility of occurrence of bifurcation is evaluated by the probability calculated.