  In this paper, we consider the Cucker-Smale flocking particles which are
subject to the same velocity-dependent noise, which exhibits a phase change
phenomenon occurs bringing the system from a "non flocking" to a "flocking"
state as the strength of noises decreases. We rigorously show the stochastic
mean-field limit from the many-particle Cucker-Smale system with multiplicative
noises to the Vlasov-type stochastic partial differential equation as the
number of particles goes to infinity. More precisely, we provide a quantitative
error estimate between solutions to the stochastic particle system and
measure-valued solutions to the expected limiting stochastic partial
differential equation by using the Wasserstein distance. For the limiting
equation, we construct global-in-time measure-valued solutions and study the
stability and large-time behavior showing the convergence of velocities to
their mean exponentially fast almost surely.
