Stochastic equations on compact groups in discrete negative time

@article{Akahori2006StochasticEO,
  title={Stochastic equations on compact groups in discrete negative time},
  author={Jir{\^o} Akahori and Chihiro Uenishi and Kouji Yano},
  journal={Probability Theory and Related Fields},
  year={2006},
  volume={140},
  pages={569-593}
}
In this paper a stochastic equation on compact groups in discrete negative time is studied. The diagonal group action on the extreme points of solutions is proved to be transitive by means of the coupling method. This result is applied to generalize Yor’s work which is closely related to Tsirelson’s stochastic differential equation and to give criteria for existence of a strong solution and for uniqueness in law.