Under appropriate assumptions on the boundary conditions and on the services, we obtain ergodic results for both versions of the model. |
In the more difficult half plane problem, the aim is to obtain evolutions which are both temporally and spatially ergodic. |
This duality structure, interesting by itsetf, is also instrumental in proving some of the ergodic results. |
For the quadrant version, we prove the existence of temporally ergodic evolutions and of spatially ergodic ones. |
While in the Harvard College Observatory he worked on many mathematical and astronomical subjects including topology and ergodic theory. |
Doeblin also contributed to the theory of random chains with complete connection, some of which was used in a paper by him on ergodic properties of continued fractions. |