Stochastic equations on compact groups in discrete negative time

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. This research was supported by Open Research Center Project for Private Universities: matching fund subsidy from MEXT, 2004–2008.