  This paper analyzes the training process of GANs via stochastic differential
equations (SDEs). It first establishes SDE approximations for the training of
GANs under stochastic gradient algorithms, with precise error bound analysis.
It then describes the long-run behavior of GANs training via the invariant
measures of its SDE approximations under proper conditions. This work builds
theoretical foundation for GANs training and provides analytical tools to study
its evolution and stability.
