Null flows, positive flows and the structure of stationary symmetric stable processes

Samorodnitsky, Gennady

Ann. Probab., Tome 33 (2005) no. 1, p. 1782-1803 / Harvested from Project Euclid

Résumé

This paper elucidates the connection between stationary symmetric α-stable processes with 0<α<2 and nonsingular flows on measure spaces by describing a new and unique decomposition of stationary stable processes into those corresponding to positive flows and those corresponding to null flows. We show that necessary and sufficient for a stationary stable process to be ergodic is that its positive component vanishes.

Publié le : 2005-09-14
Classification: Stable process, stationary process, integral representation, ergodic theory, nonsingular flow, dissipative flow, conservative flow, null flow, positive flow, ergodicity, 60G10, 60G52, 37A40

@article{1127395873,
     author = {Samorodnitsky, Gennady},
     title = {Null flows, positive flows and the structure of stationary symmetric stable processes},
     journal = {Ann. Probab.},
     volume = {33},
     number = {1},
     year = {2005},
     pages = { 1782-1803},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1127395873}
}

Samorodnitsky, Gennady. Null flows, positive flows and the structure of stationary symmetric stable processes. Ann. Probab., Tome 33 (2005) no. 1, pp.  1782-1803. http://gdmltest.u-ga.fr/item/1127395873/