In the theory of martingales, the Dubins-Schwarz theorem (or Dambis-Dubins-Schwarz theorem) is a theorem that says all continuous local martingales and martingales are time-changed Brownian motions.
The theorem was proven in 1965 by Lester Dubins and Gideon E. Schwarz [1] and independently in the same year by K. E. Dambis, a doctorial student of Eugene Dynkin. [2] [3]
Let
Let and and define for all the time-changes (i.e. stopping times) [4]
Then is a -Brownian motion and .
In the theory of martingales, the Dubins-Schwarz theorem (or Dambis-Dubins-Schwarz theorem) is a theorem that says all continuous local martingales and martingales are time-changed Brownian motions.
The theorem was proven in 1965 by Lester Dubins and Gideon E. Schwarz [1] and independently in the same year by K. E. Dambis, a doctorial student of Eugene Dynkin. [2] [3]
Let
Let and and define for all the time-changes (i.e. stopping times) [4]
Then is a -Brownian motion and .