Some measure-preserving point transformations on the Wiener space and their ergodicity
| dc.creator | Ustunel, A. S. | |
| dc.creator | Zakai, M. | |
| dc.date | 2000-02-24 | |
| dc.date | 2000-05-28 | |
| dc.date.accessioned | 2026-07-07T04:34:02Z | |
| dc.date.available | 2026-07-07T04:34:02Z | |
| dc.description | Suppose that T is a map of the Wiener space into itself, of the following type: T=I+u where u takes its values in the Cameron-Martin space H. Assume also that u is a finite sum of H-valued multiple Ito-Wiener integrals. In this work we prove that if T preserves the Wiener measure, then necessarily u is in the first Wiener chaos and the transformation corresponding to it is a rotation in the sense of [9]. Afterwards the ergodicity and mixing of such transformations, which are second quantizations of the unitary operators on the Cameron-Martin space, are characterized. Finally, the ergocity of the transformation dY_t=gamma(t)dW_t, 0 \le t \le 1 where W is n-dimensional Wiener and gamma is non random is characterized | |
| dc.identifier | https://arxiv.org/abs/math/0002198 | |
| dc.identifier | http://arxiv.org/abs/math/0002198 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58748 | |
| dc.subject | Probability | |
| dc.title | Some measure-preserving point transformations on the Wiener space and their ergodicity | |
| dc.type | text |