Hausdorff Measure for a Stable-Like Process over an Infinite Extension of a Local Field
| dc.creator | Kochubei, Anatoly N. | |
| dc.date | 2001-07-21 | |
| dc.date | 2001-11-14 | |
| dc.date.accessioned | 2026-07-07T04:42:40Z | |
| dc.date.available | 2026-07-07T04:42:40Z | |
| dc.description | We consider an infinite extension $K$ of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. $K$ is equipped with an inductive limit topology; its conjugate $\bar{K}$ is a completion of $K$ with respect to a topology given by certain explicitly written seminorms. The semigroup of measures, which defines a stable-like process $X(t)$ on $\bar{K}$, is concentrated on a compact subgroup $S\subset \bar{K}$. We study properties of the process $X_S(t)$, a part of $X(t)$ in $S$. It is shown that the Hausdorff and packing dimensions of the image of an interval equal 0 almost surely. In the case of tamely ramified extensions a correct Hausdorff measure for this set is found. | |
| dc.description | The final version, to appear in Journal of Theoretical Probability | |
| dc.identifier | https://arxiv.org/abs/math/0107156 | |
| dc.identifier | http://arxiv.org/abs/math/0107156 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61882 | |
| dc.subject | Probability | |
| dc.subject | Number Theory | |
| dc.title | Hausdorff Measure for a Stable-Like Process over an Infinite Extension of a Local Field | |
| dc.type | text |